Since the offering box was opened but once a year, the Hosts were covered with the dust and debris that had collected there. After being carefully cleaned by the priests, they were enclosed in a ciborium and placed inside the tabernacle of the main altar of the Church of St. Mary. The following day, in the company of a great gathering of townspeople, Archbishop Alessandro Zondadari carried the Sacred Hosts in solemn procession back to the Church of St. Francis.
During the two centuries that followed it has sometimes been wondered why the Hosts were not consumed by a priest during Mass, which would have been the ordinary procedure in such a case. While there is no definite answer, there are two theories. One explanation is that crowds of people from both Siena and neighboring cities gathered in the church to offer prayers of reparation before the sacred particles, forcing the priests to conserve them for a time. The other reason the priests did not consume them might well have been because of their soiled condition. While the Hosts were superficially cleaned after their discovery, they still retained a great deal of dirt. In such cases it is not necessary to consume consecrated Hosts, but it is permitted to allow them to deteriorate naturally, at which time Christ would no longer be present. http://www.therealpresence.org/eucharst/mir/siena.html