Life insurance policies can have a contingent beneficiary or contingent owner. This simply means that if something happens that the primary beneficiary or owner predeceases the insured then the policy proceeds or ownership transfers to the contingent (or secondary) owner or beneficiary. If both predecease the insured then any funds from the policy would go into the estate.
The definition of contingent is "dependent for existence on something not yet certain". In life insurance terms, it means that the contingent beneficiary exists just in case the primary beneficiary (or all the primary beneficiaries, if there are more than one) are not alive when the insured person dies. If the owner is someone different than the insured, one could set a contingent owner of the policy, as well.
Life insurance is to protect survivors from the "what if's" in life, and thus it is a good idea to name a contingent beneficiary for the same reason.
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If you are referring to a "contingent" beneficiary, it is simply the "second" beneficiary named, so that if something quite unfortunate occurred to the primary beneficiary, the contingent would be the recipient of the proceeds.
Initially, when you apply for a life insurance policy (or other contracts), these would be named.
Contingent policy beneficiaries or owner can be the second option for the proceeds of the policy if the primary beneficiaries are no longer alive or at the death of the policy owner (not also as the insured). Think of contingents as a backup option or people in reserve that would have an insurable interest in the demise of the policy insured.
Life insurance is to protect survivors from the "what if's" in life, and thus it is a good idea to name a contingent beneficiary for the same reason.
Initially, when you apply for a life insurance policy (or other contracts), these would be named.