Canadian theologian Douglas John Hall provides good insight into this communal element:
The community enacts its unity with its head its members with one another. Partaking of the one cup and the one loaf, the members, “though man,” as Paul says, affirm and are confirmed in their oneness.”
This interpretation of the Eucharist calls in question all privatistic practices of the sacrament. The communion is a corporate act, and even when it must be administered apart from the worshiping community, the latter as in the case of baptism, ought certainly to be represented. This corporateness seems to me more important than whether one regards th Eucharist from the vantage point o of the tradition of transubstantiation, the mediating position of consubstantiation, or the Zwinglian symbolic or memorial conception. The critical question is not the substantialistic one (whether the bread becomes body, where the wine becomes blood); it is, rather, the relational question: How does the Sacramental function sustain the community? (Douglas John Hall, Confessing the Faith: Christian Theology in a North American Context, Fortress Press, 1996, pp. 114-115).
Thus, the point of the Eucharist isn’t creating pieces of Jesus in the form of bread (forgive the crudity of my statement), but creating community, which reflects and embodies the person of Jesus in the world.
If the Table is a communal act, it requires the presence of community. Even when we take the Supper to the shut-in, we do so understanding that in taking the bread and cup in the home or the hospital, we gather as an extension of the larger body.
This concern for the community is reflected in Paul’s discussion of the celebration of the Supper in 1 Corinthians 11. It is in this chapter that Paul lays out the words of institution – for the first time. Paul writes:
This is why those who eat the bread or drink the cup of the Lord inappropriately will be guilty of the Lord’s body and blood. Each individual should test himself or herself, and eat from the bread and drink from the cup in that way. Those who eat and drink without correctly understanding the body are eating and drinking their own judgment. Because of this, many of you are weak and sick, and quite a few have died. . . . If some of you are hungry, they should eat at home so that getting together doesn’t lead to judgment. (1 Corinthians 11:27-34a Common English Bible).
Paul has been, traditionally, interpreted here as referring to the mystical body of Christ in the elements – thus giving rise to the doctrine of real presence and then transubstantiation. But, I think that the Common English Bible makes it as clear as possible, that the point is understanding the body of Christ as the congregation. By acting in a way that dishonors the community, leading to drunkenness and hunger, the community had dishonored the one who called them to the table. There is little of the mystical here, but much that is concerned about the behavior of those who gather at the table.