There is more to this than just the short sale or debt aspect.
Was there a will, is the property owned by a trust, is there an executor, will probate be necessary?
Technically the couple do not own the property if the lady had it in her name and she recently died. Broadly speaking I would expect the estate owns the property. There is a well defined process for moving the title to the heirs. The same process can be used to facilitate communication with the lender even if there is no Power Of Attorney (POA).
Legal advice that is specific to the situation and the state is needed to clarify just what you have on your hands.
If the lender is facing taking the property back they might be very open to a short sale or they might want to just foreclose.
As the lady has died the short sale process might be easier as the hardship conversation can be simpler. The lender really has no one to go after other than the estate if the debt exceeds what they are likely to get from sale of the property. The lender cannot come after the heirs directly.