If your primary beneficiary is deceased and you haven't named a contingent beneficiary, the money will go to your estate.
Contingent and primary beneficiaries can be changed if the policy is a revocable one, such as with many individual policies. In the business world, most policies are irrevocable, as they are only meant to insure the person(s) originally specified as beneficiaries.
Virtually any conditions may be in place for a contingent beneficiary of a will as this depends entirely on the person drafting the will.