How to fix the damaged floor of a vanity cabinet?
I don't see evidence of animals. Obviously that area was very wet for a period of time at some point, and particle board doesn't tolerate that. A little pressure is all it would've taken to punch through like we see here.
The simplest way is to fit a new sheet of material over the top of the existing floor. If you use 3/4&quot; material you probably don't need to do any repair to what's there now. Just cut it to fit inside the cabinet and extending out to the edge of the face frame. (Notch around the face frame center stile.) You may need to temporarily remove the drain trap parts to make room to finagle the new sheet in there, or even pull the countertop (with the faucet attached but disconnected from the lines).
Ideally you'll purchase a piece of shelving with a finished edge. Use that edge at the front. MDF isn't appropriate unless it's coated or varnished. It'll be a sponge for any spills or leaks.
If you don't like the idea of raising the floor that little bit you'll need to put on your cabinet maker hat. Cut away the existing floor, install small cleats all the way around, recessed the thickness of your new floor, and set in a new floor panel. That procedure is a bit much for an answer on a Q&amp;A site, so post new specific questions if you like.