When the realization that she and Tom are well and truly lost hits home, Becky’s reaction is one of extreme anguish.
She sank to the ground, and burst inot such a frenzy of crying that Tom was appalled with the idea that she might die, or lose her reason. (chapter 32)
She weeps continually throughout her ordeal, and also appears physically quite weak, for example when it is said that ‘her frail limbs refused to carry her further’(chapter 32). After their rescue, while Tom recovers fairly quickly, she languishes in bed for several days and even afterwards ‘looked as if she had passed through a wasting illness’(chapter 33).
Becky therefore does appear quite weak and even sickly, in contrast to Tom who seems to have more endurance and rationality, still making plans to try and get out while Becky allows herself to be overcome by exhaustion and fear. In this way she does appear to some extent to be the stereotype of a weak and helpless girl.
However, the sheer horror of the situation is also continually stressed. Tom and Becky are trapped without food or water or other resources and for a time it does seem that they are doomed to die a lonely and ghastly death, when even the voices of rescuers from outside pass them by. Tom is really no less agitated than Becky, but puts on a braver face. It should be remembered, too, that they are both still children; and the terrible situation they find themselves in would surely be enough to unhinge the mind of an adult. Even the evil Injun Joe, when inadvertently sealed inside the cave for good, is finally reduced to a ‘tortured’ state (chapter 34).
It is true that Becky is never as closely characterized as Tom is in the book, but she has earlier appeared as a girl of some spirit, and her behaviour, when faced with such extreme circumstances as being trapped underground, is not altogether unrealistic.