I've NEVER seen a single airline's workrules that DIDN'T have a specific restriction against leaving the layover city during a scheduled layover period without notifying movement control.

Many airlines (mainly Asian ones) used to even impose a strict curfew on their FAs on layover, requiring that they be back in the hotel by certain hours and that they not engage in "activities that may reflect badly" on the airline.

When my mother was in charge of FA training at Air India in the early 1970s, they spent an entire day on training new recruits how to conduct themselves on layovers and while off-duty but in uniform!!