Yes, an insurance company can refuse to sell a life insurance policy to a person who had cancer in the past and who has fully recovered. Businesses that sell insurance are private companies that can pick and choose who insurance policies are offered to at a certain premium will be offered to.These companies are under no obligation to offer all people who wish an insurance policy at a certain premium the desired policy.If the insurance company has denied your request for a policy, it is entirely its option to do so and entirely within its right as a private company.