When a hero dies, do you lose equipped trinkets?

My understanding is that when a hero falls in combat any trinkets they had equipped become part of the loot pool for that fight, allowing you to reclaim them if you win that fight. However, if you retreat from that fight those trinkets will be lost forever.

By extension, if all your heroes fall, then everything equipped by that group will be lost.

I'm not sure what happens to trinkets if a hero falls outside of combat (say, to bleeding).
Actually, can that even happen...? I can't remember it happening, but maybe I've just been lucky or have a bad memory...