Abuyer is assuming a loan and the loan balance has turned out to be less than the assumption balance provided by the seller. how would this be handled according to the residential contract to buy and sell ?

The buyer has the right to terminate the contract, but he/she is not obligated to do so.

If the loan balance was actually smaller than what the seller believed it to be, it means that the buyer will have to pay a larger amount of cash. If the new amount of cash is larger than the cash the buyer has, he/she has the right to terminate the contract by written notice. But if the buyer has all the cash needed, then the buyer can choose to proceed with the sales contact.

I personally believe that it depends on the difference between the estimated debt balance and the actual debt balance. If the difference is relatively small, the buyer might go on with the sale, but if the difference is too large, then the buyer might decide to cancel the deal.