How do non-refundable deposits work?

I’ve already moved out and got my money back, so this isn’t an issue I have, more of just a question I can’t find an answer to. Now, I really am curious about what could’ve happened.

I rented a place and agreed to make part of my security deposit non-refundable in lieu of paying a pet rent (ex: $1,000 deposit, $200 of it is non-refundable for the pet). This was a fair deal to me. I got my full refundable deposit back at the end of my lease no issue.

That being said, what if there was a reason to charge my deposit? Say $50 to repair something. Does my landlord have to take that out of the refundable portion? Or would I only be charged if my damages were beyond what the non-refundable portion was?