Is there a single word for "come out" as in "that stain will never come out"

Three words come to mind: disappear, vanish and evanish. Of these I suggest disappear and vanish as most commonly understood, while evanish fits your need well but is not well known. Vanish has overtones (below) of sudden disappearance that may not suit normal stain removal. So perhaps the safest choice is disappear

Cambridge

disappear:

to no longer exist

(of a person or thing) to go to a place or into a condition where the person or thing cannot be seen

Cambridge

vanish

to disappear or stop being present or existing, especially in a sudden, surprising way

to disappear or stop existing, esp. suddenly

Merriam Webster

evanish: intransitive verb

1: Vanish, disappear

2: to cease to be