This situation can be a problem for life insurance policy owners, because a paid up policy eliminates one of the common methods that family members find out about life insurance policies. For example, if the policy were not paid up, then notices would be mailed out to inform the owner of the delinquency. Without the past due notices to help you out, there are a few other things you can try.
Check through old bank balance books. The policy has not always been paid up, and there may be a record of past payments to be found in old bank records. The same is true if the deceased kept piles of receipts. It may take a while to sift through the clutter to find information you are looking for, but it will be worth the effort.
Check with any insurance companies the deceased had for other matters. Because of the savings available with purchasing multiple policies from the same company, your family member may have taken out their life insurance company with the same company the furnished, for instance, their homeowners insurance or auto insurance. There is no guarantee that you will find the missing policy this way, but it is actually a very likely thing to attempt.
You could also try sending query letters to life insurance companies, but that is tantamount to hunting for a needle in a haystack. Unless you have some information which narrows down the possible choices, there are probably too many life insurance companies to realistically check in with them all. If you do attempt to find the policy this way, start with major insurers, and ask them for any tips they may have in making the search easier. Your situation may be new to you, but the odds are good that the insurance company has been through the same scenario in the past, and they may know a shortcut to resolve the issue.