A buyer purchased a home under an agreement that made the buyer personally obligated to continue making payments under the seller's existing mortgage. If the buyer defaults and the court sale of the property does not satisfy the debt, the buyer will be liable for making up the difference. The buyer has taken over/assume the sellers mortgage.
Often, then this happens nothing about the loan changes besides who is paying for it. The payments, interest rates, and loan term agreements stay the same. Someone else just becomes financially responsible for the payments.