Life Insurance does pay for funeral expenses but the Insurance Company will require you to pay the premiums for the rest of the persons life which would mean that you'd pay more in premiums than what you'd pay for the funeral.
Some Life Insurance companies allow you to cash out on the life insurance policy before you die which is a good idea and if you've built enough cash in the Life Insurance Policy you could pay for the funeral ahead of time instead of waiting for life insurance to pay out.
To claim on a life insurance policy and get them to pay the funeral and other final expenses you submit a legit death certificate to the life insurance company who then pays out the cost to the funeral home and then pays the beneficiary the rest of the money for the rest of the final expenses.