Unwanted/Embarrassing Rescue

The Heroes go into full-rescue operation to save someone's life. After much hardship, they prevail only to learn that the victim didn't want to be rescued.

A few possible reasons:
 * The captive has a personal grudge against their would-be liberator(s) and would rather die than be indebted to them.
 * The captive was ready to welcome misery or death.
 * The captive got themself caught on purpose in order to execute a plan which the Heroes have now ruined for their side.
 * The captive is being held as bait for the rescuers and prefers to face the danger themself rather than put them at risk.
 * The captive considers being obliged to their rescuer to be more trouble than just escaping without their help or even continued captivity would have been.
 * The "captive" was actually a willing guest in the first place, and the apparent need for rescue was a silly misunderstanding.
 * An escape is just what the captors want as part of their larger plan, and the captive wants to thwart that by staying put.

The captive was already getting away or even turning the tables on their captor without help, and the "rescuers" just screwed that up by barging in. Even worse if the rescuers get in danger themselves and the captive has to get the rescuers out of it.

Examples

 * Fiona, though at first pleased to be saved, no longer wants to be after it is revealed that her rescuer is an ogre and will not leave until Shrek forces her to.
 * Woody at first wants to escape Al's penthouse and return to Andy's home, but after learning about Jessie's abandonment story, and with encouraging words from Stinky Pete, he couldn't bring himself to make an Air-Vent Passageway escape and abandon his Roundup Gang. When Buzz and his rescue team arrive, Woody tells him that he's accepting his fate as a display in a Japanese toy museum, but has second thoughts after Buzz leaves.