Their ability to foreclose is most likely written in the documents you signed when the loan closed. The property is collateral for the loan. If your don't pay, they're depending on the value of the property to insure the money they loaned you gets paid, either by your payments or a sale in foreclosure.
If the house gets destroyed and you have no insurance, they lose all of the money. Same is true for taxes. If the government auctions the house for taxes, they lose also. For those reasons, the mortgage payment includes an escrow payment that insures the insurance and taxes are paid.
Answered Aug 26, 2010
Edited Aug 26, 2010