Making 2D Tilemap Areas Impassible During Runtime?

I have a 2D tilemap, and currently my characters move in one-tile increments by checking a set of code-defined Tile objects to see if the target area is occupied and passable. That is, I'm not using Unity's collision detection or layers for pathfinding. The gameplay revolves around tiles changing their terrain type or becoming impassible as they're "damaged" and "repaired".

I recently tried the official Roguelike project and I want to revive my own project. So, my question:

If I try using a Navmesh for pathfinding, how can I change individual tiles to become (im)passible during runtime?

If I can make this work, I might be able to change from the clunky tile-based movement I have now, to smooth movement governed by Unity's colliders. It'd still be crucial to detect which tile the hero/monsters are standing on at each moment, but that could be done by doing a vertical ray, I think.