What is the ruling of Islamic law regarding a person who engaged in an illicit relationship with a married woman, then repented and cut ties with her, but she is threatening to commit suicide if he does not resume talking to her? And would he be sinful if she takes her own life?

If the woman resorts to witchcraft, there is no sin upon you. Rather, she has wronged herself by continuing the sinful relationship and insisting on communication despite your repentance. As for you, you have sinned and transgressed the boundaries of Allah by your relationship with her, and you have done well by repenting. We advise you to be cautious of returning to such relationships or being lenient in dealing with foreign women, as the Sunnah has warned against their temptation. The Prophet, peace and blessings be upon him, said: "Indeed, the world is sweet and green, and Allah is going to make you vicegerents in it, and He will see how you act. So, beware of the world and beware of women, for the first tribulation of the Children of Israel was concerning women." We advise you to prevent her from communicating with you by blocking her or changing your numbers and accounts to be safe.