The nine transfers Congress protected are mostly not sales, which is why they do not make a loan assumable in the sense buyers mean. For a loan secured by residential property of fewer than five dwelling units, 12 USC 1701j-3(d) bars a lender from exercising a due-on-sale clause on nine listed events, including a junior lien that does not transfer occupancy rights, a transfer by devise, descent or on the death of a joint tenant, a lease of three years or less without a purchase option, a transfer to a relative on the borrower's death, a transfer where the borrower's spouse or children become an owner, a transfer under a divorce decree or separation agreement by which the spouse becomes an owner, and a transfer into a living trust in which the borrower remains a beneficiary. Not one of them is a sale of the house to a buyer, and none of them releases the original borrower from the note. What the list protects is a household rearranging its own affairs, plus a handful of transactions that do not shift occupancy at all. The protection is real and it is narrow.
FHA runs the opposite policy, by regulation, and states it as a rule against restrictions. 24 CFR 203.512 is headed "Free assumability; exceptions," and its first paragraph provides that "a mortgagee shall not impose, agree to or enforce legal restrictions on conveyance... or restrictions on assumption of the insured mortgage, unless specifically permitted by this part..." The exceptions are what matter in practice: paragraph (b) allows a credit review, and permits approval only where at least one person acquiring ownership "is determined to be creditworthy under applicable standards prescribed by the Secretary," or the selling borrower keeps an ownership interest, or the transfer is by devise or descent. Paragraph (c) blocks approval where the buyer could not be an eligible substitute mortgagor because the property will not be their residence. And paragraph (d) requires the mortgage itself to contain a due-on-sale clause in a form the Secretary prescribes, which is how the policy is enforced against unapproved transfers.
Release of the seller is a separate approval from approval of the buyer, and sellers routinely assume it is included. On an FHA loan, 24 CFR 203.258 provides that the lender "may effect the release of a mortgagor from personal liability on the mortgage note, only if it obtains the Commissioner's approval of a substitute mortgagor." On a VA loan the release runs through 38 USC 3714, which requires the holder to approve the assumption and relieve the seller of further liability where the seller notified the holder in writing before disposing of the property, the loan is current, and the purchaser has assumed full liability by contract and "qualifies from a credit standpoint, to the same extent as if the purchaser were a veteran." A seller who lets a buyer take over payments informally, without the holder's approval, has transferred the property and kept the debt.
USDA is the clearest case of approval and release being different questions, because its regulation refuses the release outright. 7 CFR 3555.256(b) requires Agency approval before a lender consents to a transfer with assumption, and then sets the conditions: the transferee "must assume the entire outstanding debt and acquire all property securing the guaranteed loan balance; however, the transferor must remain personally liable," and the transferor must pay any interest-subsidy recapture owed at the time of the transfer. The same section provides that where a property is transferred with the lender's knowledge and the debt is not assumed, Rural Development will void the guarantee, outside a short list of family transfers the regulation exempts. A seller of a USDA-guaranteed home should assume they stay on the note and price the deal accordingly.
The VA entitlement trap is the sharpest thing on this page. Release from liability and restoration of entitlement are governed by different provisions and are not the same event. Entitlement is dealt with at 38 USC 3702(b), which lets the Secretary exclude previously used entitlement in specified circumstances. The circumstance that applies while the loan remains outstanding is (b)(2), where "a veteran-transferee has agreed to assume the outstanding balance on the loan and consented to the use of the veteran-transferee's entitlement... in place of the veteran-transferor's." The other routes require the loan to have been repaid in full or the Secretary to have been released from liability on it. So a veteran who sells to a non-veteran buyer under an approved assumption is off the note and still has their entitlement tied up in a house they no longer own, which limits what they can borrow on the next one until that loan is eventually paid off. A veteran selling with an assumption in mind should ask specifically whether the buyer is substituting their own entitlement, because the answer changes the seller's next purchase and is not the same question as the release.
What actually stops most assumptions is arithmetic, not eligibility. The buyer takes over a balance, not a purchase price, and has to produce the difference. On a house that has appreciated or on a loan that has been paid down for years, that difference can be larger than a conventional down payment, and it has to be found in cash or in a second loan at current rates, which erodes the blended cost the low first-rate promised. Assumptions also take longer to process than a new loan, and the agency's approval sits on the critical path of the closing. An assumption carries its own processing charge, and on a VA loan that charge is set by the same statutory funding fee table that governs new loans.