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
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