Buying homes from motivated sellers...what happens to their "problems" when the home becomes yours?

[Miles Stanley]

so say you approach a potential motivated seller to buy their house and relieve them of their financial issue (cant make payment, etc).  You make an offer, close on it for the agreed amount and boom, its yours!

When the property becomes yours, what happens to that mortgage that was attached to the property?  Also, what about other things like liens, etc?

Probably a dumb question, but I'm learnin' here! : )

Thanks,