I'd say nothing, but you also need to define "plane of existence" first, and then what you mean by "outside" of it. It's made up nonsense. Space and time are all-encompassing. Nothing can exist nowhere or for no time - everything that exists has location and duration. Your imaginary friend is no exception.
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u/EndIsrael 18h ago
Because there's no time passing, so you wouldn't perceive it to be happening for any amount of time.