Is it permissible for my mother, who is unable to fast due to old age and illness, to pay the fasting expiation (kaffarah), and what is its value and how is it paid, and are there other ways besides payment, and is it permissible to pay it from ill-gotten wealth?

Fasting is an obligation for anyone who meets the conditions of its incumbency. If your mother did not fast in the past despite her ability to do so, and without a trusted doctor informing her of her inability, then she must repent and make up for all the Ramadans she missed. However, if her not fasting was due to unusual hardship or based on a doctor's report about the danger of her illness and her permanent inability, then her breaking the fast is permissible, and she must pay a fidyah (expiatory payment) for each day. This fidyah is a mudd (approximately 750 grams of rice) of the staple food of the country, given to the poor and needy.

The majority of scholars hold that the fidyah should be given in food, while some scholars permit giving it in cash if that is more beneficial for the poor. It is permissible to pay the fidyah daily or to postpone it until the end of the month. It is not permissible to pay it before Ramadan or for a day before its dawn. The fidyah is the only way to absolve the responsibility of the incapacitated person, and it is not valid if paid from unlawfully acquired wealth.