One outlet does not appear to be attached to a breaker in the breaker panel. Only in shutting the main breaker off does that outlet lose electricity. Is this dangerous? Is there a remedy?
Definitely dangerous. The main breaker is for a very high amperage (like 100 amps). If there's no other breaker between the main breaker and the outlet, a high amperage would be needed to trip it.
I doubt the wires to the outlet could be sized appropriatedly. And I doubt it is allowed to have a regular outlet on a high amperage breaker.
Maybe a sub-panel or a breaker you missed ?