For the source text click/tap here: Bava Kamma 110
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If one steals from a convert and swears falsely to him, and he (the convert) died (without leaving any heirs), he pays the principal and chomesh (the extra fifth) to the Kohanim and he brings an asham to the Altar, as it is written: But if the man has no kinsman to whom restitution may be made for the guilt, the restitution for guilt which is made shall be for Hashem, for the Kohen, aside from the ram of atonement, whereby atonement shall be provided for him. If he was taking the money and the asham up (to Yerushalayim), and died, the money shall be given to the robber’s sons, and the asham shall graze until it gets a blemish, and it will be sold and its money shall fall to the free offering coffer.
If he gave the money to the men of the mishmar and he died (without bringing the asham), the heirs cannot take the money from their hands, as it is written: Whatever a man gives to the Kohen shall be his. If he gave the money to (the first mishmar of) Yehoyariv and the asham to (the second mishmar of) Yedayah, he has fulfilled his obligation (for the money is supposed to be given before the asham is brought on the Mizbe’ach).
We explore the history of the mishmarot from the Chumash and Tanach through to the medieval Piyutim until the Cairo Geniza fragments.