If its a very dense tight weave pile, and a shrinker, then I take it the pile must be synthetic, possibly Polypropylene. On the stairs as a runner, then that is usually a sign, especially given the type of property, that it is a good quality carpet. Are you sure its not Wool? If it is wool then it is unlikely to be a bad shrinker. If Polyprop then use an Alkaline pre spray and rinse, as that would get it clean with less wetting than a splitter and acid rinse, and wont do the fibre any harm.
Dave.