In order to buy life insurance on someone else's life, you need Insurable Interest in the person you want to insure.
Usually, insurable interest exists between family members.
Insurable Interest means you rely on the person for some means of financial support, or that you would suffer a financial loss should the person die.
For example, adult children may have insurable interest in their parents, because their parents are paying fro their college education.
Yes, insurers may allow you to buy life insurance on a family member.