Question: What becomes of Communion Hosts after Mass?
Answer: It has long been the custom of the Church to keep Hosts consecrated at Mass for the Communion of those who are sick or otherwise seriously impeded from attending Mass. Once consecrated, the Eucharistic elements become the true Body and Blood of Christ for as long as they retain the "appearances" of the original bread and wine. The normal practice in Catholic churches is to keep a large number of Hosts in the tabernacle on the main altar, reserved in the golden cup-like vessel called the "ciborium." This serves to insure that all of the uncertain number of communicants may receive on Sundays and feast days. In small parishes on weekdays, the priest may consecrate a number of Hosts based on his assumptions about who will communicate, and the faithful may receive a Host consecrated at that Mass, a practice considered generally desirable by the Church. If his assumptions leave him short of Hosts, he will take more out of the tabernacle. If he finds himself with too many Hosts, he is likely to receive Them himself; morally a part of his own Communion, even if separated from It by a few minutes.
The Sacred Host is the Body and Blood of Jesus Christ, no matter whether it was consecrated minutes, hours, days, or even weeks ago. The claim of Modernists that a Host from the tabernacle is somehow a "leftover from a previous meal" is clearly a profession of Infidelity, a repudiation of our Lord's Real Presence in the Blessed Sacrament. For many of these heretics, the Blessed Sacrament is reduced to the level of "a symbol of the community" -- which community they erroneously raise in their minds to the level of the real Body of Christ. Priests that send their altar boys out to bury "excess hosts" or who pour "extra wine" into the sacristy sink very likely hold a non-Catholic understanding of the Mass and the Blessed Sacrament.
Priests responsible for the reservation of the Blessed Sacrament are required to see that the reserved Hosts are given in Holy Communion (or received by the priest himself) long before they might begin to become inedible. Only in extreme cases (e.g. if the consecrated elements have begun to biologically decompose and loose the appearances of bread or wine, or if they have become noxious because of something added to them) may they be disposed of in the sacrarium or the ground -- and then only after allowing them to be fully diluted or decomposed. The possibility that something might thus go wrong with the materials of the Mass is covered in a rather comprehensive section of The Roman Missal, "de defectibus."