In this situation, the lender forecloses and sells the property. If they don't recover the amount owed from the sale, there is what is called a deficiency. That's the difference between the total amount owed and what was recovered from the foreclosure sale. In some states, the lender is allowed to pursue the deficiency. In others, the lender only gets the property. If your father's house was in one of these states that allows deficiency collection, what likely happened is the lender sold the right to collect the deficiency to a collection agency.
You or your father need to track down exactly what happened. The amount owed should be close to what the bank sent him in the foreclosure notice. The auction price should have been recorded. If either the lender or the collection agency went to court and got a deficiency judgement, a record of the case exists.
The collection agency must provide him with proof that the debt exists, that it is his, and that they have a right to collect it. The debt is not secured by property so the collection procedure is similar to any other unsecured loan. A judgement must be obtained and enforced. If the debt has been sold, the collection agency provides proof, and they threaten to sue, then action should be taken. In his shoes, I would consider retaining a bankruptcy attorney. The idea is not to file, but to have the attorney tell the collectors that he will file immediately if they obtain a judgement. That generally removes the motivation to pursue the case, and often it's dropped (or sold off to another collector). It also stops all discussion. When the collector calls, the answer is I have retained a bankruptcy attorney and his number is...