[The Grammarian]

Out of curiosity, what do Catholics do with it? Particularly, what do they do with it if they leave it alone long enough that it becomes moldy?

[AnAmericanMother]

Any remaining Precious Blood is consumed by the priest. The chalice is then rinsed with water and the water poured down a special sink (the "sacrarium") in the sacristy - the drain line runs into a dry well so that the earth receives any traces of the Blood rather than the common sewer.

Any remaining consecrated Hosts are reserved in a pyx in the Tabernacle (usually behind the high altar but sometimes in a separate chapel).

Because the wafers used for consecration are very thin, very crisp, and have minimal sugar content, they do not usually go moldy. If they were to do so, though, they would be dissolved in water and likewise poured down the sacrarium.