This is a crossover of Invader Zim and Lilo & Stitch, but Lilo isn't in it. I'm pretending that 626 landed on an asteroid rather than Earth, and that's where the story begins. I have a few ideas, but I'm not certain about where I'm going with this yet.
DISCLAIMER: I don't own Invader Zim or Lilo & Stitch and I dislike romance.

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"Where are we goooooing?" GIR asked into the side of his master's head, a goofy grin on his face.

Zim and GIR were in the voot cruiser. They had left Earth a half an hour ago. The flourishing blue planet could still be seen through the corner of the window.

"WHEEEERRRREEE?" GIR repeated louder.

Zim had an annoyed look on his face, having opened his mouth, but he wasn't given the chance to reply before GIR asked again.

"WHERE?!"
He leaned back, away from Zim's face, of which he was done screaming into.

"I told you GIR, we're going to pick up a supposedly powerful experiment... thing I found. It- he's going to demolish the humans and their cities in exchange for cover," Zim explained for the second time.

"WHHHE-"

"An asteroid, GIR."

It was less than an hour earlier when Zim received a call from someone saying their name was '626' and claiming to be capable of mass destruction. 626 said he was in dire need of a place to hide from some authorities. Zim agreed to take 626 back to Earth on the condition that he destroy at least one human, but Zim was skeptical and had plans to deceive the strange alien later whether 626 proved to be useful or not. Zim was curious to see if the experiment was telling the truth about what he could do, since it was somewhat hard to believe. The whole thing was GIR's idea, really. He convinced his master to make the deal with 626, charmed by the 'squishy blue, four-armed koala'. For this reason, it was odd that GIR was asking where they were now headed... But, then again, this was GIR.

They landed on the asteroid minutes later. The window opened and Zim jumped out of the cockpit, wearing a maroon colored space suit. The window closed behind him. A jell-like bubble slid over his head, then turned completely transparent. There was a flexible tube attached to his suit and the ship. GIR stayed in the voot cruiser.

Zim was standing in the wake of a large, bright red crashed ship that had been buried half way into solid rock due to impact. There was smoke coming off of it. Broken parts were shattered across the asteroid's surface. It made him wonder how the pilot could have survived, let alone any machinery within the damaged ship used to contact him.

"Where are you?" Zim asked sternly as he walked towards the ship.

A blue bug-eyed head popped up from behind the ship. It was the easily recognizable 626. He had a satisfied grin on his face and gave a low chuckle, eyes narrowed deviously. He was an odd looking thing with an enormous blue nose, a big mouth full of stubby yellow teeth, and long ears sticking out of the sides of his head. He was wearing a red suit. He was about a few inches shorter than Zim, and a lot rounder.

Zim lifted a brow. "You're 626?" he began, scrutinizing the alien.

"Eh," said 626 in reply, motionless.

Zim looked to one side, then back at 626. "I'll take that as a yes. Before we depart, care to demonstrate one of these 'powerful abilities' you said you posses?"

626 frowned. He wanted to go before the council found out where he was. Surely they could track the police cruiser he stole and would already know where it crashed. He needed to get off of the asteroid and away from the cruiser as soon as possible, which left him in the desperate situation. He could simply steal this alien's ship, but he was interested in this person's hiding place on Earth and wouldn't know how to get to it. Not only that, but who knew how his ship worked. It probably wouldn't be hard for 626 to figure out, but he might as well save himself the trouble in this situation.
"Eh, Eh," he said impatiently, then dropped down completely blocked from view behind the ship. He bent over forward and dug his front claws under the police cruiser to get a good grip on it, then pulled it up right out of the rock, pulling up dozens of smaller chipped rocks with it. In a few seconds, he was able to lift it above his head and looked at Zim, holding the police cruiser up with ease.

"Impressive!" Zim said with a grin and tilted his head slightly. "Get whatever you're taking. We go now."

626 dropped the police cruiser hastily. He didn't have anything he wanted from it. He walked around it, then jumped into the cockpit of Zim's voot cruiser when the window opened. He stood near Zim's seat. Once Zim was inside, the window closed and they took off, heading back to Earth.