Author's Insights:

So, when I was first reading through the Visual Novel, it kind of bothered me that down the "Superhero" (More accurately translated, "Hero/Ally of Justice") path, Sakura is implied to have died.

But we later find out canonically (in the non-bad end continuation) that she had been listening, and that she had escaped.

Now, you could argue that maybe once Shirou had decided to let Sakura die, she had come to terms with it and let Tohsaka kill her. And sure, maybe that is what happened.

But given her state of mind, I think she'd be more liable to still run away. At the very least, to personally seek out Shirou to ask him to kill her.

So this is essentially a subvariant of both the "Superhero" (Day 9) ending and the "Happy End" (Day 13) Ending.

Starting from the "Superhero" END, if Sakura still ran away and Shirou found her, and from the resulting changes that would occur on Day 13 (The "Happy End" choice).

Everything else between those days happen almost exactly the same way, though.

...

Rider doesn't kill Shirou because of these aforementioned changes.

...

Sakura and Rider mini-story summary:

About 30 minutes before Shirou comes in to kill Sakura, Sakura and Rider have a talk.

Sakura knows that just ordering Rider with a command spell wouldn't be that effective if Rider disagrees, so they talk first. And Sakura tries to convince Rider that for her, killing her would be saving her.

She also tells Rider that if Rider kills her senpai, then Sakura will kill herself or order Rider to kill her shortly afterwards. Rider disagrees, both with her idea of salvation and with her methods, but reluctantly accepts Sakura's terms.

Sakura then orders Rider with her last command spell,

"Please, Rider. This is my last will. Please, protect senpai until the very end."

Rider accepts, and hides in the shadows, until Shirou comes in.

She had a strong urge to stop him, or, at least to cut off his hands as he was strangling Sakura. But given Sakura's last will and her last words to him, and seeing Shirou's tearful despairing face as he was doing it, she couldn't bring herself to move.

Rider was ultimately disappointed in his choice, and his character.

But even so, she continued to faithfully protect him until the very end of the Holy Grail War, as her master willed.

Sometimes directly, sometimes indirectly. But ultimately, she was the one who, for better or worse, kept Emiya Shirou alive and got him through his Holy Grail War as its victor.