NetHack panics when it reaches a state where it is completely impossible to continue the current session by terminating the game immediately with the messages "Oops... Suddenly, the dungeon collapses.", sometimes generating a backup saved game if the game can be recovered to a point where it is continuable.
It is very rare for a normal game to result in a panic; however, several bugs in NetHack 3.4.3 revolve around panics, usually involving monsters or objects being destroyed under unusual circumstances; exceptions include C343-23, "Dungeon collapses after vault guard fails to lead you out.", and C343-383, "Applying a bullwhip while hero is at edge of map may cause a panic or crash."
Less serious errors can result in an impossible message.
There's even a rumor about this.
- They say that collapsing a dungeon often creates a panic.