Legal Question in Wills and Trusts in Illinois

Maybe, maybe not. Depends on your relationship to the decedent, when the named beneficiary died and what contingent beneficiary provisions are contained in the pension contract. If this is truly a pension plan and not a retirment account we would not expect anyone other than a surviving spouse to be able to inherit, unless there were funds on hand that represented the decedent's contributions to the plan,

While your question is not clear, if you are the administrator of the estate of the deceased beneficiary and have been so appointed by a probate court, then you should be able to recover funds due the decedent from the pension, if any. Whether the pension pays out beyond death and to whom is a matter that needs review. If the funds are due to the estate, once you recover the funds it will be your duty to distribute them through the proper administration of the estate.