Many people only take out enough basic life insurance to provide their beneficiary or beneficiaries with enough money to cover the cost of a funeral. Supplemental life insurance offers a higher payout so that beneficiaries receive a lot more money to help stabilize financial affairs after a policyholder dies. In many cases, supplemental life insurance is taken out by workers via an employer-sponsored option where the employer has made arrangements with an insurance company to provide workers with a discounted premium rate. Of course, supplemental life insurance is also offered to individuals by insurers outside of employment scenarios.
There are a lot of details that you fail to include with your question. For example, did the policyholder take out the policies through the same life insurance company? Do these policies name the same or different beneficiary or beneficiaries?
If the insurance was taken out through two different companies for some reason, then the payout dates are entirely up to the separate insurance companies. Even with policies taken out through the same company, departmental and back-end processes might result in two separate payouts. Two different beneficiaries would also result in separate payouts on likely different dates.
Another situation you don't mention is bankruptcy. If an employer sponsoring a plan or insurer go bankrupt in Missouri, a beneficiary or beneficiaries can still receive benefits from basic and supplemental life insurance policies that were kept in good standing before the bankruptcy. That said, one or both policies would be paid out by the Missouri Life & Health Insurance Guaranty Association that protects policy beneficiaries in this type of situation. As with an insurance company, you might receive the monies from a supplemental policy at the same time or not. If the two policies are through two separate companies where only one is bankrupt, then you will obviously receive the benefits at two separate times since two separate entities would then handle the claims. For more information about bankruptcy coverage, visit the Missouri Department of Insurance FAQ page.
Your best course of action at this time is to speak with the insurance agent or agents who helped set up the policies. If those agents aren't available, then you should contact the customer service helpline(s) associated with each policy for more details.