Eternal city theory (spoilers)

This a theory and I could be wrong but I've been thinking about this.

I replayed it like 3 times by now and it's about Cinder. I felt something was off, he was all for joining the cagers but suddenly changed his mind. I don't think he's in city cause when MC suggest to go far from the city, cinder said it's not possible. and I'm not sure if he can survive on his own? Maybe he can. I chose to look for him and he's nowhere to be found, esp if mc knew his secrets spots in the city.

So, is it me or did he go back to the caretakers to become a apprentice. When mc and the others tried to escape. Bazor told Cinder he was gonna have him as an apprentice if they stayed. So what if he did went back?

What do you guys think?