Ehh I got fired once, the new hiring manager would have to know the manager I reported to be able to find out. I actually had a different manager at the same company ask me if I was interested in coming back becasue he didn't know a different manager fired me.

You need to be memorable enough too.

Backchanel is not really a real concern unless you did something really fucked up.

Otherwise who do you think knows?

It depends. If you're in a niche industry/specialization then people might know each other.