When you (the PC) dies, you become an unhoused soul that can re-inhabit your corpse pretty much at will. As for others in the Shadowlands it seems to vary somewhat. Constructs that die become unhoused souls that wander until collected or imprisoned, and the House of Constructs has what they call an "Essence Vault" where souls are stored for use in other constructs. When an unhoused soul "dies" it essentially discorporates into raw anima and seemingly disappears, either destroyed entirely or passing into yet another form of existence we know nothing of.