Yes, you can buy life insurance on another person, but their are guidelines that insurance companies follow in allowing someone to purchase life insurance on another person.
Usually, a life insurer will require that you have an "Insurable Interest" in the person you want to insure for life insurance. And, the insurer may or may not require the person's permission or signature on the application for life insurance.
Insurable Interest means that you either rely on the person for financial support or that you may suffer some financial cost as a result of the person's death.
So, for instance, if your parent died, you may have to pay for the funeral costs if you parent did not have any money or life insurance.
Insurable interest does exist between parents and their children, spouses, siblings, family members, and business partners, among others.
To learn more, read this article ---> Who Can You Insure for Life Insurance?