If I owned MHA, Bakugo would be backlisted. However since I don't, I gotta have that happen here. But I'm getting ahead of myself here after all since that's just half of the plot. The other half follows a depressed and revenge filled Izuku as he takes down crime as an anti hero named the Underdog using very evil methods.
Watch as our beloved green haired ball of determation loses the will to always walk the straight and narrow path and instead walk the line and decline into the dark.
It all started on that fateful day after Bakugo destroyed Izuku's hero book and when All Might said he couldn't be a hero. Both event's cracked Izuku's metal state and drove him to his new life of crime and heroism that filled the gap he lost that day. So with all of that out of the way, let's get right down to it and start the show off with a left turn right off the bat with one simple word. Shall we? :)

Izuku looked at All Might with a smile but hid his anger well. He didn't want to deal with this again. Was he being taunted right now by All Might's offer with his words from their first encounter this afternoon? Izuku wasn't gonna take another fause attempt at a chance so he cut off his former icon before he could feed more lies to Izuku. "No." Izuku said, stopping All Might in his tracks.

"What? No? But I'm offering you a chance at your dream young man. Don't you want it?" All Might asked. Izuku shook his head as his hair covered his eyes. "I said no.
I'm done with being tossed around and discarded like a ragdoll, so take your offer and shove it." Izuku told the now shocked Number One Hero as he walked past him and towards his home. This was the moment Izuku's life changed for the better in an unexpected way. He just didn't know how yet. Once back home he went straight to his room without speaking to his mom, Inko Mydoriya. (Writers Note: I dislike Inko. I just feel she could have been a better mom and actually just let her son have his moment even if it's just to make him feel happy. So anyone wants to send me a message saying she's not so bad, go right ahead. I've made my point and it really shows.) Once in his room Izuku locked the door and started making plans to sell everything All Might related he owned. He'd need as much money as possible once he left his mom behind. Tomorrow was the start of the eight month gap between now and high school. He'd be ready for that too. As he marked the items online he wrote some plans and would take them into effect ASAP.

He opened a spare notebook and wrote everything down. He labled them as steps but they doubled as rules.

*Step 1: Sell everything and collect the money. It should take a few hours for my account to get everything but it's worth both the wait and effort.

Step 2: Leave home and start fresh. It'll hurt mom but I don't care anymore, it's better this way.

Step 3: Fake my own death. Easy enough with the right know how.

Step 4: Ensure I find work and remain hidden. Anything that can help I'll use.

Step 5: Establish my new persona and start off small. Loose clothing will make me more agile and faster. I'll need weapons to defend myself too. Some hand to hand and sneak attacks wouldn't hurt either. Maybe a firearm could be a last resort if I'm feeling outmatched. There are a number of heroes that will try to find me once I'm well enough known so I'll need to be at least three steps ahead in order to stay on top of the game. The more infomation I have, the better off I'll be in the long run. I'll also need to discard my original name and burn everything related to it to improve my chances.

Step 6: Take Kac- Bakugo down! He's my prime target and will regret everything he's ever done. The selfish and intitled prick will want to die by the time I'm done with him. And I'll start with the task of getting him blacklisted. Heh, better said then done but then again, isn't everything? His complex to always be top dog is my best weapon. His downfall will be my most wonderful satisfaction and once that happens, I'll be truly happy for the first time in a very long time.

Step 7: Find any allies I can use and have them be in a close knit group to have at arms reach. An eye for an eye goes a long way if you play your cards right.
I'll need to do some favors for the more dangerus villians but I'm gonna play if safe until I'm confident that I can handle them.

Step 8: Don't kill! I won't cross that line. If I do, I'm the worst of the worst and will be resorted to ending my own life so I can redeem myself. I'm still willing to help those in need as long as I'm sure they can't help or defend themselves. Some good karma and word will help establish my rep as an anti hero and not as a villian. I need to keep my morals in check after all.

Step 9: Steal to survive only. Small and petty crimes are the least harmful. That way, I can keep my hit and run tactics going. Having a few different places to lay low will be benifical in my plans. The more spaces I have, the better.

Step 10: Have at least five back up plans and have them be unique enough to be nearly impossible for anyone else to understand wthout the right amout of intillgence and understanding of another language. I'm thinking binary code is my best choice given it's 1's and 0's only pattern.*

With that, Izuku closed his new book and began to plan his next step by leaving during the night. He'd check his sales once he was ready in a few hours before leaving.
If everything goes right he should have at least a few hundred thousand yen to use. He then decided to take a shower and would be ready to enjoy his last meal with his mom. He loved her of course but also felt that she could have been a better parent. Izuku couldn't place all the blame on her of course. Half of it went to his dad who left shortly after Izuku was born. The greenie often wondered where his dad was, be decided to just forget him and move on. There's no point in thinking anything about a deadbeat who abandoned his family. Once out of the shower and freshly changed into a set of grey clothes and white socks he entered the living room where Inko was setting the table. They were having fried rice with a healthy mix of vegtables added in for good measure. Inko turned to face Izuku and took note of the sadness and cold look in Izuku's eyes. She hesitated fora second before putting on a smile and spoke to her son.

"Izuku, are you alright? H-how was school today?"

'She's nervous, perfect. I can get some sympathy points and milk this just for fun. Alright, time to put on the sadness act.' Izuku thought as he switched his cold stare to a slight frown. "Not good mom. Kacchan burned my hero book." Izuku said as he took a seat at the table. "I'd show you, but I don't wanna look at it anymore."

Inko felt a wave of grief for her son wash over her right now. His hero books meant the entire world to him and that fact that his former ex best friend would do something that evil was just another point that Izuku should give up on his dream of being a hero in Inko's mind. She wanted her son to be safe but also worried for him too. What could she say other then try to make him cheer up? She might be doing the best she could but that wasn't always gonna be enough. Inko had to try though,
she had too! "Izuku, it's gonna be okay. We can get you a brand new book. Two even!" Anything she could say to help her son out was worth it not matter how usless it was! She was about to futher talk when she was stopped by Izuku rasing a hand.

"Mom, thanks but it's okay. Really, I can just keep the ones I have and move on. It's not like I'm able to attend U.A. right?" He darkly joked as he flashed a sad smile before digging into his dinner. "Thanks for dinner by the way mom, it looks amazing." Izuku told her before he resumed eating. Dinner was silent the entire time and Izuku prefered it that way. Inko on the other hand wasn't feeling like eating. Her son looked broken. She was out of ideas and had to keep trying! Maybe they could make a day of tomorrow? If anything it should help Izuku a tad. "Izuku," Inko said, casuing her son to stop and look up at her. "why don't we spend tomorrow together and do whatever you want?"

Izuku smiled and shook his head. "Thanks mom but I'll be needing some alone time. Sorry." Inko frowned again but nodded in understanding.

After dinner Izuku hugged his mom and went back to his room. He explained that he just wanted to sleep and Inko understood, promising to be ready to talk at anytime he wanted. Little did she know is that would be the last time she'd talk to her only child. He was aleady in step two of his plan and making a bed double to give him a little extra time. Any advantage he'd have to aid him in his plans, he'd take. Six hours later after Inko went to bed Izuku got started with step two. He had the bed dummy in his bed and gathered up his supplies. He wouldn't be able to take/steal much, depending on how you felt about the situation. He grabbed a few bottles of water, a few cans of food with a can opener, some fruit bars of different flavors and a spare flashlight he had in his room incase the power went out. He grabbed a few outfits that weren't All Might related, which was harder then he expected it to be given almost everything he had was All Might related. He did find a set of black boots that were brand new from last year. He just never got around to wearing them since at the time the All Might Mk III brand sneakers had just come out and Izuku just had to have a pair. It was actually Inko who suggested the idea and he agreed for her sake. He still wore the grey get up and put on the black boots plus another brand new item of clothing Inko insisted he get;a green hoodie that matched his hair and eyes. Hey, Inko may be a bad mom but she can have her good moments too from time to time. He put it on and after a moment of looking in the mirror he decided he liked the new colors. He checked his sails and his eyes nearly bugged out of his head once he saw the number for everything sold that was on the screen. It read: 250,000 yen! Izuku knew that was a lot but would have to make do and save as much as possible for as long as possible to stay afloat and fund his plans. He knew everything would freak Inko out but decided to leave it like it was and on his way out after double checking everything Izuku locked his door as he walked out and did the same with the enterance door. He was ready to start his new life alone and wasn't gonna give up on his new path in life.