26 Year Old Zombie Mortgage

This is gonna blow some people's minds. My wife and I inherited a house two years ago in Alabama. It went through probate just fine and we were never notified of any liens or mortgages on the house. The deed was transferred to my wife via a probate judge.

Two years after probate we are contacted via mail by Specialized Loan Servicing. They sent a notice of default and intent to forclose. The total balance is around 35k with interest. Here is the kicker. There hasn't been a payment made since 2010. We got the original loan paperwork from the county and it was taken out in 1998 for 20k.

My questions are... Why wouldn't they have forclosed in 14 years if they could? What debt collector in their right mind wouldn't have taken a home worth 400k over a 35k debt if they could?

What are my options here? We basically got a dream home for free and we really want to keep it. It is a 3 bedroom 2 bath beautiful brick home in the middle of nowhere. It appraised at around 400k. I only make about 20k a year and have a terrible credit score because I've literally never used my credit. My wife has a 703 though but is unemployed. So I'm not sure I would get approved for a home equity loan to pay them back. They want 24k in arrears. I have not yet contacted them to negotiate because I want to get all my ducks in a row. We have until June 18th to respond.

Also, what can I do to hold them off while I try to come up with the money to pay it all at once?

I'm terrified to lose our home, any help would greatly be appreciated.