Certainly, it would be a lot harder to get a new mortgage underwritten, which makes refinancing mostly impossible and makes selling difficult.
Given that the property would be difficult to sell, I'd imagine even if the contract allows it, lenders wouldn't foreclose for lack of insurance if insurance is unavailable.
Really, I think the way to move forward on the issue that so many homes are built in areas they shouldn't be is to make available insurance policies that cover permanent relocation, rather than rebuilding in place. You can still live there until it burns down, at which time, you must move elsewhere and the lot is deemed unbuildable for the forseable future. With some sort of provision to manage windfalls from changes in conditions allowing safe construction in the future. (It's not fair if you force people out, but ten or twenty years later, let people in again; OTOH, maybe one hundred years later, it will make sense?)