Symbolism, Imagery, Allegory
It's just what everyone wants: to find out there's an unlocked secret passage leading into their room. Yeah, Em's not too thrilled about that. But that unlocked door symbolizes her vulnerability in Udolpho and outside in the greater world. She has no parents, no money, and an evil step-uncle who plans to do who knows what.
Please, Just Ring the Doorbell
When Em tells Montoni that the unlocked door is a problem, he doesn't believe her—or really care, to be totally honest. She has practically no power at this point, so she's just forced to deal with it. But when Count Morano actually uses the secret passage to break into Em's room, she's more scared of ghosts than an actual living creep:
Certain remembrances now struck upon her heart, and almost subdued the feeble remains of her spirits" as the ghostly figure approaches her bedside. (2.6.104)
See, Em's not really sure what kind of threats she's up against. Does she need to worry about Morano, or does Montoni have him under control? And is Montoni trustworthy? How about Barnardine, the sketchy porter? Em's not sure who's coming through that secret door, but she's totally defenseless from every angle. As long as that door remains unlocked, she's sure to have problems.