Most times life insurance does cover someone's funeral and other expenses if the person committed suicide but you really have to read the terms and conditions of the life insurance policy that you or someone has taken out on the person or yourself.
Usually the Life Insurance Policy won't cover suicide for a person if the Life Insurance Policy has only been in effect for 2 years or less.
Most life insurance companies will pay out on the death of someone if they committed suicide if the Life Insurance policy has been in effect for 2 years or more and you've never missed a payment or been cancelled.
So it's really up to the individual life insurance company and their policy as to whether they will cover the cost of a funeral or other expenses if someone commits suicide.