She will be required to sign the application, attesting to her health and answer some health questions. She may also be required to take a physical exam to qualify for the life insurance coverage.
The life insurance company may investigate in the event of an untimely death, for example, if you mother died within the first two years of being insured under the life insurance policy.
However, if you are named as the beneficiary of the life insurance policy, and your mother is insured, and passes away you would receive the death benefit from the life insurance policy, as long as you weren't the one responsible for your mother's death, or she didn't commit suicide within the first two years (one year in Colorado). There may be some other exclusions that apply to the life insurance policy.
Here's how you can learn how to buy life insurance online.