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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.
Because damage remains marked on a creature until the damage is removed as the turn ends, nonlethal damage dealt to a Sliver may become lethal if Sinew Sliver leaves the battlefield during that turn.
Sinew Sliver's ability does give itself +1/+1.
