Identity is a spiritual aspect that can be stored in the metal aluminum (as a Feruchemical ability), or which can be used to wipe out internal Allomantic reserves (as an Allomantic ability), or which can be used to steal Enhancement Allomancy via spiritweb (as a Hemalurgic ability).
When an object is recovered - or worse, destroyed - in the Physical Realm, it's Identity changes and the spirit returns to the location of, its body. Abandoned objects that had been owned for a long while , so they had a strong Identity, but that currently had nobody in the Physical Realm to care for them, were best.
Some readers have theorized that Hoid has a pre-Shattering pseudo-Feruchemical ability that lets him store only spiritual aspects (i.e., Investiture, Connection, Identity, and Fortune). He's been observed using Investiture, Connection and Fortune, so there's some merit there, but readers won't know for sure for a while.