wow thats a good question. my gut says that they are still monsters and can be targeted and damaged or squished like a monster in the stash. as long as the card doing the damage or squishing doesn't refer specifically to the stash or "hired".
for example
elvish-impersonator could damage combo rat and squish it.
but like
/crash-and-burn or
rain-of-death wouldn't be able to deal damage to a monster stuck to another card.