What do you lose if you die in Egg Heist?

Extraction is the line that matters. Everything you pick up only becomes yours once you get out with it, so going down before that point wipes the whole haul rather than part of it. There is no partial credit for a run that went well right up until the last fight.

Fainting is treated the same as dying. There is no soft version of it that costs you only the loot. The backpack goes, along with everything inside it, and the gear you had equipped when you went down goes with it.

That last part is what changes how you prepare. An Egg Heist run puts your own kit on the table, not just the run's takings, so the better equipped you go in the more a single bad fight can take off you. Deciding what to bring is a real decision, and the safe version of it is bringing less.