Whole Life Ins. Question

Hi, Whole Life Insurance: Should a policy holder die before the total amount of the insurance policy is paid up(example.. $3,000.00 for whole life w/out med. exam, with monthly payment of say $32.00/month). Should the policy holder unexpectently fall ill and die say 11/2 yrs. later,is it the responsibility of the beneficiaries named to pay the balance of the policy to the ins.co.holding the policy??
If the beneficiaries have to pay the balance, then why does one need ins. to begin with. It would be more beneficial to save $32.00/month in the event of the death, rather than have them pay another bill(the balance) and burden the children.
Maybe I am missing something, but if this is the case, doesn't pay to have any kind of life ins. at age 74. Your thoughts please and no sales pitch please. Just answers.
Thank you and God Bless you during this Holy Lenten Season.