In a non-recourse state (or, to a lesser extent, even in a recourse state) foreclosure on an underwater mortgage loans isn't a great deal for the bank; it either eliminates any chance on recovering part of the mortgage (non-recourse), or turns the amount above what can be realized in a foreclosure sale into a non-secured debt (recourse). Depending on circumstances, there's a chance they'll just choose not to do that for a very long time (much longer than would be the case either with an "above water" mortgage that wasn't being paid, or than a landlord would float a tenant that wasn't paying.) They also have a pretty big incentive to approve a short sale on an underwater mortgage, since you'll probably get a better price than a foreclosure sale and cost them less money than foreclosing and trying to sell.
(Have I been underwater, gone an extended period of time withput paying a mortgage both while living in the home and then after moving out, getting a buyer, and proposing and waiting for approval for a short sale, in a non-recourse state? Yes, yes I have.)
That works both ways. Google "underwater mortgage"