Not unless they are claiming the person on a joint return such as married filing a joint return. Married filing separately cannot; both parents after a divorce cannot; a person's parents and that person cannot.
Also, if a person is letting someone else claim them as a dependent because they are living with the person and that person is taking care of them, either that person can claim themselves, or the person taking care of them, but not both.
Also, if a person is letting someone else claim them as a dependent because they are living with the person and that person is taking care of them, either that person can claim themselves, or the person taking care of them, but not both.