My sincere condolances if there has been a loss in your family. Any assets that were in the name of the decedent with no other owner or beneficiary no belong to the decedent's estate. Proceeds from the estate would be distributed based on the direction of the will (if there is one). The Probate Court would name an executor (title varies based on state law) who has the responsibility for distributing the funds. Depending on the size of the estate, some states (including New York) may allow for the completion of a "Small Estate Affidavit. If the surviving spouse is entitled to the funds, he/she can ask the maker of the check to reissue to the him/her. More specific questions about probate/estate law should be directed to an attorney.
If the checks are payble to two individuals (i.e. John Doe or Jane Doe) then the survivor can deposit them.
A bank should not allow a check payable solely to the decedent to be deposited into any account other than one titled "The Estate of John/Jane Doe."
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I can do all things through Him who gives me strength. (Phillipians 4:13)