They don't expire. There's no "claim by" date. As long as the policy was active at the date of death, the insurance company is obligated to pay.
Now, the longer you wait to claim, the harder it potentially is to track down the company responsible for paying the claim. For example, a company operating 40 years ago might have changed names and telephone numbers a half dozen times. Also, they might not have a copy of the old policy, if someone stopped paying for it 30 years ago - you would need to provide a copy of that policy.
In most cases, the insurance company has no way of knowing that someone is deceased. They don't, for example, do a search every month of every insured person to see if they died. They usually find out about the death, when a claim is filed. If someone DOES die and no beneficiary can be located, the money is paid to the ESTATE of the deceased - it doesn't go into unclaimed property funds. The estate of the deceased, however, CAN go into unclaimed property.