Strategies of buying "subject to"

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I'm trying to wrap my head around when it make sense to buy a property "subject to".  What are the typical exit strategies after buying subject to?  Let's say a seller won't accept 50K on a 100K property.  If they only owe 60K, do you offer them a subject to deal for 60K?  Seems like if 60K cash doesn't work for you, then 60K subject to won't either.  

Or, do you not offer a higher purchase price if doing subject to?  If so, then why would the seller ever agree to it for the same price?

I'm obviously missing something here because I know it's a popular way of buying.

Also, who makes the payments to the bank when it's a subject to deal?