Is a Muslim held accountable if he severs ties with a foolish person who is verbally abusive or who backbites him, by avoiding him and not greeting him, or not inviting him, or not accepting his invitation?

The basic principle is the impermissibility of shunning a Muslim for more than three days, unless there is a legitimate Shariah reason, based on the Prophet's (peace be upon him) saying: "It is not permissible for a Muslim to shun his brother for more than three nights." However, it is permissible to shun for more than three days if associating with the person brings harm, deficiency, or damage to one's religion, self, or worldly affairs. Furthermore, shunning people of sin and desires is مطلوب (required/desirable), unless the interaction is for the purpose of inviting them to guidance and directing them. Greeting a person and avoiding them as much as possible exempts one from the prohibited shunning, based on his (peace be upon him) saying: "If three [days] pass him, let him meet him and greet him." And in shunning people of sin, the overriding benefit should be considered.