The Byzantine Rite churches have a ritual that is open to all.
See, our eucharist bread is cut from a loaf, but the entire loaf is not used, only a central section.
The remaining outer section, which has been blessed, but not placed on the Holy Table, nor consecrated. This outer section, at the end of the liturgy, is diced, placed in bowls, and shared with all the faithful, often disregarding whether Catholic/Orthodox or not. It is called the antidorion. Traditionally, it is customary to make a small donation as well, and the antidorion offering is used for some good works.
(Now, in some regional uses of the Byzantine Rite, the outer portion can be cut up and consecrated if the Lamb, the central section, isn’t sufficiently large to provide for the faithful. In others, a second loaf is instead used… with that much more for the antidorion shared right after the liturgy!)
