You are looking for an assumable mortgage. That seemed to be a thing a few decades ago, but there still may be some available. Some FHA, and VA loans are assumable.
This is from the Veterans Administration:
One feature of the VA home loan is that is assumable.
This means that anyone can assume, or take over payment, on a VA home
loan, if they qualify. It is a unique feature that gives you the
option to purchase a home with a previously set interest rate or, in a
time of need, avoid foreclosure. There could be a situation where you
are unable pay back your loan or maybe you are simply unable to sell a
home in your area. In any case, this feature of the VA home loan is
meant to serve your needs.
Why would this be a benefit to you?
- When interest rates rise, assuming a low interest rate VA home loan could make the home more desirable to a purchaser
- The funding fee (unless exempt) is only 0.5%
- A Veteran can substitute their own VA home loan entitlement to assume your loan, thereby allowing VA to restore your entitlement,
assuming the other Veteran has enough entitlement to cover your loan
- Anyone, even a non-Veteran, can assume your loan, but in such case your entitlement remains with the loan
- Any equity in the home remains with the loan, however you can negotiate with the buyer on cashing out some or all the equity as part
of the sale
VA home loan assumption requires servicer approval, and in some
instances VA approval. Be sure to work with your servicer to obtain
approval for assumption. They will usually perform an income and
credit check to be sure the assumer is a good risk and is not likely
to default on the loan
This is from the FHA When Is An FHA Loan Assumable?:
When is an FHA loan assumable? Let’s start by examining what the FHA
single-family home loan handbook, HUD 4000.1, defines as a loan
assumption. “Assumption refers to the transfer of an existing mortgage
obligation from an existing Borrower to the assuming Borrower.”
An FHA loan assumption is generally possible-for most FHA loans closed
today, the lender’s participation and approval will be required in
order to carry out a loan assumption transaction.
There are still forms required, and the servicer has to approve the switch. They will still look at the buyers income and credit history to make sure it can be afforded.
Trying to do the switch informally is very risky, if one party stops making payments everything collapses. If the lender finds out the assumption wasn't approved they can demand immediate payment of the mortgage balance.