In most places the 2002 General Instruction of the Roman Missal gives the impression that priest, deacon and concelebrants should drink what remains of the Precious Blood. For example, from the 2002 GIRM approved for the USA, which can be accessed from
romanrite.com/girm.html:
“182. … If Communion is given under both kinds, the deacon himself administers the chalice to the communicants; and, when the distribution is completed, he immediately and reverently consumes at the altar all of the Blood of Christ that remains, assisted if necessary by other deacons and priests.”
But it has in n. 284:
“b. Whatever may remain of the Blood of Christ is consumed at the altar by the priest or the deacon or the duly instituted acolyte who ministered the chalice. The same then purifies, wipes, and arranges the sacred vessels in the usual way.”
The justification for the other EMHCs (besides an instituted acolyte) doing this is from this part of the USA GIRM:
“283. … In all that pertains to Communion under both kinds, the
Norms for the Distribution and Reception of Holy Communion under Both Kinds in the Dioceses of the United States of America are to be followed (see nos. 27-54).”
This document gave the permission, for other EMHCs to do this, in the USA.