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This is the lesser shown part of the holodeck program.
We know they experience this because Moriarty learned to summon the arch.
It’s been a while since I saw the ep, but wasn’t Moriarty stuck on because the computer was asked to create an opponent that could beat Data and it got caught in a weird loop? I’m pretty sure Moriarty was a major exception in some way, none of the other constructs are self aware and all get turned off with the program