Once cleared there is no respawn of mobs in either the crypt or cave, only mushrooms. After the H&H update crypts got the single skeleton guard respawning outside every few days. I'm assuming normal anti-spawn items will prevent that.
Here's a cave I completely dug out from its surroundings. The 'magical' entry into the cave continues to work even from below. In this example it'd be easy to build a small camp/base underneath and access the cave interior when you need to go afk. What I don't know is if trolls with the tree trunk club can penetrate the permanent cave structure with their AOE like they are supposed to be able to do with regular terrain walls.

https://steamcommunity.com/sharedfiles/filedetails/?id=2678982380

https://steamcommunity.com/sharedfiles/filedetails/?id=2678977195