The slivers would survive, even at the expense of every other creature on Otaria.

Essence Sliver

Whenever a Sliver deals damage, its controller gains that much life.

Secret Lair Drop

Time Spiral Timeshifted

Legions

You only gain the life when the triggered ability resolves. If you are reduced to zero life before the ability resolves, you will lose before gaining the life.

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.

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.