Assign for how much??!!

I'm trying to research the whole assignment process and I can't figure out this part: Does assigning only work with people whose homes are completely paid for or in other words they do not have a mortgage, and for what ever reason just want to get rid of the property? ...Because I'm feeling like I'm missing something when I read that someone buys a house for say $50k then sales it/re-assigns it for $55k, would only about $50k is left on the mortgage which is why they'll take that amount/came up with that amount, or would the mortgage already be paid and they only want about $50K just to have the cash? OR, if there is a mortgage on the property, it would be taken care of when the investor sales it for the FMV (after he fixes it up). Thanks for taking the time to read this. I really appreciate all informing responses.