Downplayed: Princess Alice would happily kick the asses of her captors and take names afterwards, if she wasn't greatly outnumbered by her kidnappers, who are all heavily armed and have her imprisoned within a practically inescapable prison. Since she's more practical than suicidal, she figures it's probably more sensible to wait for rescue rather than try to break herself out.
Princess Alice is wheelchair-bound so she's pretty much defenseless against a physical attack.
Princess Alice lived a sheltered life, and doesn't have the skills to defend herself or escape without guards.
Inverted: Alice is the Action Girl who saves anyone in danger.
They don't kidnap her because they know she's an Action Girl.
Enforced: "The Big Bad needs to be established as such. He has to Kick the Dog is a way that will affect Bob on a personal level and give him a justification to chase after him. Let's have the Big Bad kidnapp his girlfriend!"
Invoked: "We need a hostage worth good money. Princess Alice is in no position to defend herself; capture her."
Princess Alicia deliberately goes down to the crime-ridden docks and is captured, giving the king's men an excuse to break into the house of the high-ranking noble who is the head of the kidnappers' guild.
Princess Alys goes into bandit territory to haggle with the bandit chief, knowing he is treacherous — and that her capture will sort out The So-Called Coward and Miles Gloriosus among her suitors.
Defied: Princess Alice has been trained in self-defense, so she dispatches those sent to capture her and never ends up imprisoned in the first place.
Discussed: "You can't expect Princess Alice to save herself... she's badly outnumbered and she's had no weapons training."
Conversed: "Can't this Alice even hit the Big Bad with a vase or something? Her uselessness is getting annoying!"
Princess Alice is kidnapped by the Big Bad, and gets put through some sessions of Break the Cutie, in which the Big Bad tells her that his Evil Plan only works because of her utter helpnessness. Bob saves Alice, but the trauma of being unable to do anything while Bob risked his life to save her has severely scarred her. She breaks up with him because she doesn't want to be The Load anymore.
While being kidnapped, Alice is beaten, starved,brutally raped, subject to horrific and innovative experiments, and god knows what else. By the time Bob reaches Alice, she is a gibbering, Body Horror-ridden trainwreck.
Alice has been kidnapped or her mentality was put in distress that she really needs help or saving... and nobody wants to save her, despite her pleas, because everyone else is too busy to mind their own business.
After a long while of nobody answering, finally there comes Bob the Selfless Hero arrives on the scene and takes it upon himself to save her from distress... regardless of his other schedules.
Alternatively, fed up with the lack of help, Alice decided to stop whining and pleading, and tries escaping herself, success or failure be damned, at least she tried!
Played For Laughs: Princess Alice getting kidnapped is a total Excuse Plot to get the story going, and happens every Tuesday, like clockwork. Princess Alice is quite resigned to this, and greets each kidnapping with a sigh, wiling away her hours in the dungeons.
Played For Drama: Princess Alice being kidnapped is a devastating experience for her, Bob (her rescuerand lover), and the people of her kingdom. Each time it happens, Bob goes through much angst over allowing her to be taken again, and Princess Alice gets progressively more insecure in her own power each time she allows herself to be taken, which impedes her abilities as a ruler.