Nearly-Headless Nick tells Harry, "I know nothing of the secrets of death... I believe learned wizards study the matter in the Department of Mysteries."
Assuming that Nick is referring directly or indirectly to the veil that Sirius fell through, it's entirely reasonable for the veil to be a connection, gateway, portal, whatever, to another plane: the plane where people go when they die. The veil is possibly an experiment by such 'learned wizards' trying to contact the dead or make a connection to this other plane. In this case, as Sirius didn't die from Bellatrix's spell, but merely from crossing the one-way gateway into this other plane, then the whispering voices that Harry hears are the voices of the dead, and this leaves the 'veil' open for later contact with Sirius - assuming that if one gets close enough, he or she can actually talk with the dead.