Can a debtor come after spouse's sole and separate property?

In many cases, yes, but it depends on the state that you live in. Because of a legal designation called the "the doctrine of necessaries", in many cases spouses are responsible for the other spouse’s medical debt, even if the spouse dies. The largest determining factor is how your state treats the “doctrine of necessaries”.

Common law has historically assigned to a husband the duty to provide for the necessary expenses of his wife, and in most cases, visa versa, especially these days where most households are dual-income. However, as there is also variation from state-to-state regarding debt collection.  Additionally, NV is a community property state.  

You should consult with an attorney from your state as to potential liability.