How does a person sign an unpaid mortgage over to another person without having to refinance the home?
I will try to do the best I can answering this question although one aspect of it is unclear to me: "unpaid."
Does this mean that the current mortgagor of the property is in some sort of financial distress that has prevented payment? I'm going to assume for the most thorough part of my answer that that is the case, and then address other potentialities at the end.
Only very few lenders and very few loan programs allow someone to "assume" a mortgage. Several government sponsored loans, such as FHA, are assumable in certain cases. The key to someone assuming another person's loan is that the person taking over the loan must qualify just as if they were buying the house in the first place. The only benefit can be that equity in the property can be used in the place of a down payment.
Nine times out of ten, the solution to this scenario will be for the new buyer to simply buy the home, or be placed on the title of the house and then refinance it into their name only. But BE CAREFUL! A lot of people will tell you it's no big deal to add someone onto the title of a house and drop another person off. They tell you this as if it's a casual thing that's "no big deal." What most of the people giving this advice don't realize is that almost every lender has verbiage that prohibits this.
In the lender's note, there's usually something to the effect of:
"if all or any part of the property or any interest in the property is sold or transferred without lender's prior written consent, lender may require immediate payment in full of all sums secured by the security instrument." What that means is that if you " deed someone onto title" and the lender finds out about it, they might force you to pay your loan in full or refinance.
So the bottom line is before any change in liability on the loan can take place, the lender must be involved, either to permit someone to come onto title, or to prequalify someone assume the mortgage. Keep in mind that the mortgage and the title are two separate things. If the lender allows someone to come onto title, that doesn't put them on the mortgage, nor does it remove the original owner. The only way to accomplish that goal is to see if your loan is assumable or have the interested party complete a purchase of the property.
Now to answer the other potential meaning of "unpaid" which could be taken to mean, "payments are no longer being made because the home is owned free and clear." I'm assuming that this was not the intended question, but here is the answer to that for the sake of posterity.
If someone owns a house free and clear, in almost any case, they are welcome to add people onto the title as see fit as permitted by the deed of trust, HOA (home owner's association, if any), or CC and R's, (covenants, conditions, and restrictions). Once the new person is added onto the title, the original owner can give up his or her interest in the title.