How will L2s behave if there is a PoS and PoW chain?

So it's clear to me how a fork basically works. At the time of a fork there are two consensus groups each supporting one of the chains. So at the beginning both chains will be identical and then go their own ways aka. everything that you own on the original chain before the fork will exist on the forked chain afterwards as well.

What's not clear to me atm is how L2s fit into this. For example: Will there be only on Polygon that is always the L2 of the original chain even after a fork? Or will there be like a Polygon for the PoS chain and a Polygon for the PoW chain?

Maybe it's useful for my understanding to first explain how a L2 connects to an L1 in general. That's admittedly unclear to me as well.

I hope you can help me understand that and sorry if the answer to this question is very obvious. ^{^}