Unfortunately a client was quit claim deeded a home form parent before death so they do not get the stepped up basis. But if his child inherits the home after he passes does the child (if the rules have not changed) get the FMV at the date of his death or because it was deeded to him at the original purchase value, that is the value the child gets?
How much before death was it quit claimed? I think if it was shortly (like within 6 months?) before it won't apply and you will get the step up. Usually it is a mistake to give the child the house or put them on the deed before.
Implied life estate. Here's the Code section: 20.2036-1
If it applies, they get the stepped up basis.
To your specific question, each transaction is treated separately, so if Adam quit claims the house to Bob, and then Bob dies and Charlie inherits the house, Charlies gets a stepped up basis no matter what Bob's basis was.
I agree that in the specific case you describe, the client should investigate the concept of an "implied life estate."