Does my mother, whose husband passed away, observe an iddah period after a 20-year abandonment during which her husband did not provide for her, and his saying to her: "Forbidden to you"?

The default presumption is the continuation of the marital bond. The mere abandonment of the mother by the father for a long period, or his saying to her: "You are forbidden to me," or her advanced age, or his failure to financially support her, does not nullify the marital bond unless her divorce is proven. Therefore, she must observe the waiting period (iddah) of widowhood, which is four months and ten days, as stated in the Almighty's words: "And those who are taken in death among you and leave wives behind - they, [the wives], shall wait four months and ten [days]." (Al-Baqarah: 234). The waiting period begins from the time of death, calculated in lunar months, as stated in the Almighty's words: "Indeed, the number of months with Allah is twelve [lunar] months in the Register of Allah [from] the day He created the heavens and the earth." (At-Tawbah: 36). It is forbidden for a husband to abandon his wife or cease providing for her without a legitimate religious reason, based on the Prophet's (peace and blessings be upon him) saying: "It is sufficient sin for a man to neglect those whom he is responsible to support."