They got a new mortgage on the house, using the new bigger and better house as collateral for a large loan. Can't make those payments, then they take the collateral (house.)
If you do a big makeover on a house, even if it's paid off, the city or town will raise the property taxes on it to reflect the new value of the home. For example: we put new windows, doors, and a deck on our house and the taxes went up because it upped the value of the house. There is a process a home owner can go through to contest the city's property value assessment, but in our case we would have to have a private appraisal and that cost about $400 here.
If you don't pay the taxes the city will take your house and auction it off for the taxes owed. I've seen people loose their house over $1000 of unpaid property taxes. It sucks. My FIL buys these types of homes, sometimes for like $200, then fixes them up and re-sells. He makes money off people's bad luck, with is crappy IMO, because it is usually old people that loose their home like that in this area.