Yes, they can "take" your house in the sense that they could go through the process of suing you and - if they were successful - they could put a charge on the house.(posted 8017 days ago)That scenario relies on you not successfully resisting their attempts to sue you though.
But... there are two other issues to take into account when you think about buying a house:
1. Neither I nor anyone I know can think of a reason why anyone should be buying a house right now. The market is looking like it is going to burst.
2. Applying for a mortgage is the same as applying for any other form of credit in that it will scatter details of how much you earn and what you spend in MCL Software's databases, possibly Experian and Equifax's databases. Scattering that kind of income and expenditure information around is a bad thing for anyone who is facing a shortfall claim because it could make that information available to others in certain circumstances.
Lee