What would be the point in that? If I die without paying it all, would the life insurance company take money from my accounts and then give my family the money on the life insurance policy?
No, you're confusing life insurance with a savings account.
Insurance, including life insurance, is a bet, whether or not you'll die while the policy is active. What you pay in, versus what they pay out, are the "odds".
Everyone who's paying in this year, the vast majority of those people aren't going to die. The one who does, collects the "pool" of money that pays out the death benefit on their life insurance policy to their family (beneficiary).
Insurance is basically a "sharing of risk of loss" where the risk is shared among a whole bunch of people, thus costing each of those people - who probably won't use that insurance this year - a much smaller amount of money.
You pay premiums for your life insurance policy and if you die your life insurance company pays out the death benefit to your beneficiary. However, there may be some exclusions on your life insurance policy for which they may not pay out a claim.
Here's how to learn more about how term life insurance works.