Values Dissonance: When Edwin's mother is telling him about the night Jane supposedly tried to kill Blanche, she describes the worst part - read: worse than trying to murder her own sister - as being found in a hotel room with a man she didn't know. Sort-of lampshaded by Edwin in his retort:
Jane. Poor, poor Jane. Wracked by guilt over something she never did.
Jane as a child qualifies too. It's strongly implied that their father pushed her into show business and allowed her to become the arrogant brat she was. He never disciplined her and made Blanche think she was The Unfavourite.
Blanche, over the course of the movie, culminating in her supposed death at the end.
There's more than an element of Jerkass Woobie in both cases, however. Blanche because she tried to kill Jane and then framed Jane for trying to kill her, and Jane because whether she was guilty or not, she still spent a significant amount of time psychologically tormenting and abusing her disabled sister.