When a permanent phases out, it is treated as though it doesn't exist temporarily — but it never actually changes zones. According to CR 702.25m, phasing out doesn't cause any triggers that check for a permanent 'leaving the battlefield' to trigger, and phasing in doesn't cause 'entering the battlefield' triggers to fire either. The permanent simply ceases to be seen by the game momentarily.
Death triggers specifically look for a creature dying, which is defined in CR 700.4 as being put into a graveyard from the battlefield. Since a phased-out permanent goes to a phased-out state rather than to the graveyard, it hasn't 'died' by the game's definition, and no death trigger will fire.
Similarly, 'leaves the battlefield' triggered abilities (covered under CR 603.6) require the permanent to actually change zones. Phasing does not change zones (CR 702.25b), so those triggers don't see the event at all.
Concrete example: You control a creature with a death trigger (like Midnight Reaper) and another creature phases out due to Teferi's Protection. The phased-out creature's temporary disappearance does NOT trigger Midnight Reaper's ability, because no creature moved to the graveyard.
Note: If a phased-out permanent would be destroyed or otherwise removed from the game while phased out, different rules may apply, but standard phasing alone never triggers death or leaves-the-battlefield effects.
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.