To be honest, I’m going to assume that they are being moved out of ReplicatedStorage at some point, which allows them to run. They’ll be in replicated storage just for organisational reasons
Then, do localscripts can continue running also when moved out of ReplicatedStorage for a moment and get back again? I forgot to say the script printed: it’s is still in ReplicatedStorage.
Do they have a RunContext property in the Properties menu? If so, they aren’t LocalScripts, they are normal Scripts with their RunContext set to Client. This allows it to run anywhere, even in ReplicatedStorage, but like a LocalScript in that it runs Client-side.