Or possibly physically damaged the missile enough so it no longer homes in on its target, but without actually destroying the missile's ability to maintain powered flight.
With incoming AShM, one has to score a hard kill to garranty the missile won't get you. A soft killed missile might already be a terminal trajectory when "killed", and the riddled corpse of the missile would simply glide unguided into the target by its momentum.
Physical damage to the missile would be "hard kill".
Soft kill systems ares designed to confuse incoming missiles with electronic counter-measures, decoys, smoke, flare, chaff, IR or laser jamming, etc.