Are you saying that the top of the stairs is exposed to the elements and there is living space directly below them?
If so, then in fact the stairs are a ROOF and need to be built to the same standards as any other ROOF. Slathering
goop on top of the treads (as it seems has already been done) is pretty much a waste of money. The goop-sellers
and the goop-appliers will of course have a different opinion.