The leftovers are put in the Tabernacle. Some are taken to the sick and elderly who can’t attend Mass. A priest has to concentrate it but it can be distributed by a Eucharistic minister.
Plus there is this thing called Adoration where the Tabernacle is opened for a bit and people pray in the presence of the Eucharist. One of my grandmother-in-laws goes to Adoration frequently and has an annoying habit of stopping by the other grandmother-in-law’s house to announce where she is going so everyone knows how devout she is.