Slip Out the Back

Any continuous effects with a “for as long as” duration, such as that of Extraction Specialist, ignore phased-out objects. If ignoring those objects causes the effect's conditions to no longer be met, the duration will expire.

As a creature is phased out, Auras and Equipment attached to it also phase out at the same time. Those Auras and Equipment will phase in at the same time that creature does, and they'll phase in still attached to that creature.

Choices made for permanents as they entered the battlefield are remembered when they phase in.