If you have children with your ex-spouse you may be able to buy life insurance on his life because you stand to lose financial support if he were to die.
In some states, a divorce decreement may require your ex-spouse to carry life insurance with you or your children as the beneficiary so the kids are provided for if the ex-spouse dies.
There must exist an insurable interest between you and the ex-spouse in order to buy life insurance on your ex-spouse. If you would suffer financial loss from your ex-spouse's death, there may exist insurable interest, and you may be able to buy life insurance on him/her. Learn more about insurable interest.