How can the lender know the value of home?

That's the appraiser's job. The appraiser comes out, looks at the house to see if there are any obvious problems (like, "missing roof" really lowers the value), then gets recent sale prices for "comparable" homes, and uses all that to come up with an estimate of what the current market value is.

If they foreclose, then they don't really care what the value is. They know what the loan was, and they put it up at auction. As long as they get at least that, they're happy. If they get less, then it's still a debt the former homeowner owes them. If they get more, they're supposed to give the surplus to the former homeowner, but in practice, there won't be a surplus.