Cults of many ancient cultures, including the Syrians, Phoenicians, Israelites, Greeks, and Romans, disposed of their sacred sundries in Favissae. A favissa is a cellar or pit beneath a temple, in which cultists dispose of votive offerings and worn-out ritual objects like broken clay figurines. Often objects that had fulfilled their ritual purpose would be intentionally broken before being discarded in the favissa. Discarded figures are believed to represent the deity associated with the cult. Archeological evidence suggests that such practices date far back into the neolithic period.
[...] archaeological finds reflect three major types of figurines that appear simultaneously in all assemblages, just as we have seen at Dor: an adult male, represented as a king sitting on a throne or standing, or as a warrior on a horse; a fertility goddess holding her breasts or a child and sometimes pregnant; and young boys.
Occasionally, a find will point to a particular cult practice. For example, from Greek sources we know that the Phoenician cult practiced sacred prostitution. In the first Dor favissa, we found an almost intact figurine of a naked woman with swollen belly and drooping breasts, seated with legs apart and smiling. This figurine is unique in Palestine, although two similar, but not identical, figurines have been found in Kharayeb, farther north on the Phoenician coast. In the Kharayeb examples, the woman sits with her legs apart, one hand on her knee and the other pointing to her genitals.
What we have been describing might be called the official cult, associated with sanctuaries where priests doubtless officiated. But side by side with this official cult was a popular religion or “popular cult” [...] Archaeological remains from this popular religion include such items as demonic figurines and masks [...]*
So, add a favissa to the temples in your game, and stock it with broken ritual objects—objects which could provide information for the characters and flavor for the game.
(This is for the A-Z Blogger Challenge.)