What takes place after Communion? Remember this document is an “instruction on worship of the Eucharistic mystery,” not a 100% liturgy piece.
38. On those who partake of the body and blood of Christ the gift of the Spirit is poured out abundantly like living water (see Jn 7:37-39), provided communion is received both sacramentally and spiritually, that is, in living faith that works through love. [See Council of Trent, sess. 13, Decr. de Eucharistia cap. 8: Denz-Schon 1648.]
A spiritual attitude is to be cultivated: seeking after union with Christ not only in the Eucharist, but in daily life. In the life of a group of persons, believer, such a searching “should” produce external fruit.
But the union with Christ that is the reason for the sacrament itself is to be sought not only at the time of the eucharistic celebration but is also to be prolonged all during the Christian’s life. This means that the faithful of Christ, dwelling constantly on the gift they have received, should live their daily lives in continual thanksgiving under the Holy Spirit’s guidance and should produce more abundant fruits of charity.
In order to continue more surely in the thanksgiving that in Mass is offered to God in an eminent way, those who have been nourished by communion should be encouraged to remain for some time in prayer. [See Pius XII, Encycl. Mediator Dei: Acta Apostolicae Sedis 39 (1947) 566.]
Presumably, this would be remaining after the conclusion of the celebration of Mass, and not just refraining from an early departure.