Is it obligatory to maintain contact with a sister who does not fear Allah, does not pray, steals, lies, engages in backbiting and slander, has suspicious relationships, and previously stole the mother's gold, which psychologically and financially harmed the family, especially since she does not acknowledge her wrongdoing and the questioner believes that maintaining contact with her is pointless?

The Shari'ah commanded maintaining kinship ties and forbade severing them. It did not prohibit maintaining ties with a fasiq (transgressor) or mushrik (polytheist) relative.

It is obligatory to maintain ties with your sister, advise her, explain the danger of her current state, help her with beneficial books and tapes, and frequently supplicate for her guidance.

If she does not heed the advice, and if boycotting her serves as a deterrent from the evil acts she commits, then there is no harm in boycotting her. In fact, it becomes obligatory to shun her if that is the determined path to her reformation.

A believer should have a broad heart towards sinners, hoping for their guidance and repentance. This does not contradict his denunciation of evil and his hatred for disobedience.