Step one is to speak to the family about their intentions for the property. Sometimes, other family members have emotional or nostalgic reasons to want to keep the home. They would be entitled to maintain the mortgage or seek some arrangement first.
Next, if they want the house to be liquidated, the bank would require the home be listed by an agent to draw in the highest possible offer before they would approve a short sale. Their obligation is to take the smallest loss possible and the only sure way to determine this is to get the home on the market at a reasonable price.
If you are willing to pay enough to clear the mortgage, then the estate may be willing to work with you directly and the bank wouldn't have any say in the matter. Your offer may have to be the full remaining loan balance plus all the seller's closing costs. If the property won't appraise for this you'll need bring in additional cash beyond your down payment and closing costs to make up the difference.
I hope this was helpful.
At this point, I believe the seller needs to go to the bank and get their options. Each bank is different. If you are dealing directly with the seller, you should at least have an attorney handle the transaction.