What is the ruling on severing ties of kinship with siblings who mistreat their sister and her husband, and falsely accuse them, while the sister has previously made unsuccessful efforts at reconciliation, and she is suffering from illness?

If you are ill and cannot bear the harm inflicted by your siblings when trying to mend ties with them, you are not obligated to do what harms you. Instead, you can communicate with them in writing and by phone, offer simple gifts, and visit them if you are safe from harm. Severing ties of kinship is a heinous matter in Islam. The one who maintains kinship is not the one who reciprocates good, but rather the one who maintains ties even when they are cut off by others. Seek your reward from Allah, for whoever maintains kinship and shows kindness to them despite their قطع (severance) and إساءة (ill-treatment), will have a supporter from Allah.