After divorce, should the parents and/or siblings of the ex-husband continue to pay alimony and child support to the ex-wife if the ex-husband dies?
First determine what is the likelihood of this.
Many terminal illnesses today are curable or can be put into long remission, eg. cancer.
An organ transplant might solve the pressing health problem.
No, the family of the ex-husband will not do it except if they are extraordinarily kind.
You need to plan and prepare for yourself and your children.
If the ex-spouse is a normal person, he or she will prepare for the living spouse and children so they will not be left destitute.
If the ex-spouse doesn't care about them, then you need to be prepared to protect yourself and your children.
Consult a professional about this, if you know your spouse has a terminal illness.
Don't count on in-laws, especially if they are not known to be charitable people.