No, you can't buy life insurance on just anybody.
The life insurance company will require you to have an "Insurable Interest" in the person you want to insure for life insurance.
Insurable Interest means you rely on the person for financial support, or stand to lose money if the person dies.
Insurable Interest does exist between spouses, siblings, parents and their children, relatives, and business partners, among others.
So, for instance, you may insure the life of your parent, but you will need your parent's permission, signature on the application for life insurance, and your parent may need to answer some health questions.
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Who Can You Insure for Life Insurance?