The buyer is not the only party to benefit from an assumable mortgage. The seller shares in the arbitrage by either charging a higher price for his or her home, requiring the purchaser to pay the closing costs the seller may incur, or demanding cash payment for one-half of the buyer's savings over an agreed-upon time-frame. For example, if the current interest rate is 8%, the assumable mortgage rate is 5%, and the buyer plans to live in the home for five years, the seller might demand half of the often-undiscounted expected savings for the five-year period. In such a case, the assumable mortgage may benefit the seller even more than the buyer!
Finally, VA and FHA loans may be assumed provided that the buyer receives credit approval from the mortgage lender. This contingency is not placed upon the lender, who agrees that the loan may be assumed, but rather is a way for the lender to determine if the buyer is credit-worthy. In such cases, the seller will not receive any of the arbitrage profits, but the buyer must pay additional fees to the VA or FHA.
For more on this topic, read What is an Assumable Mortgage?
This question was answered by Justin Bynum.