Green’s Dictionary of Slang

(US campus) to become unaware, as if asleep.

1980		Eble Campus Sl. Fall 5: phase out – be adversely affected by a situation; to fall asleep; to misunderstand: ‘I phase out during classes’.
1996		Eble Sl. and Sociability 30: In college slang out is the most productive particle: [...] phase out ‘become unaware, as if asleep’.