If Vampiric Sliver is put into a graveyard from the battlefield at the same time as a creature dealt damage by another Sliver, the Vampiric Sliver’s ability will trigger for the other Sliver. That Sliver will get a +1/+1 counter.

If a Sliver doesn’t have this ability when it deals damage, but does have it when the damaged creature is put into a graveyard, the ability will trigger.

If a Sliver has this ability when it deals damage, but not when the damaged creature is put into a graveyard, nothing happens.

If the creature type of a Sliver changes so it’s no longer a Sliver, it will no longer be affected by its own ability. Its ability will continue to affect other Sliver creatures.

Abilities that Slivers grant, as well as power/toughness boosts, are cumulative. However, for some abilities, like flying, having more than one instance of the ability doesn’t provide any additional benefit.