Rather, in the context of 1 Co. 11:17-34 means to effectually remember and thus show/declare the sufferings and death of the Lord by manifesting its effect, that of unity with Christ and each other, redeeming souls and purchasing them with His sinless shed blood as the body of Christ.
Take heed therefore unto yourselves, and to all the flock, over the which the Holy Ghost hath made you overseers, to feed the church of God, which he hath purchased with his own blood. (Acts 20:28)
Which means that to remember the Lord's death is to show it, which here is by sharing food with fellow members of the body, confirming that they are such and as soul "bought with a price," and which thus are to be holy and caring for each other as members of that body of Christ, thus showing union with Him and each other.
For as often as ye eat this bread, and drink this cup, ye do shew the Lord’s death till he come. (1 Corinthians 11:26) For ye are bought with a price: therefore glorify God in your body, and in your spirit, which are God’s. (1 Corinthians 6:20)
Which holiness and caring union is so much emphasized by Paul in particular, as one who used to be persecute Christ by mistreating its members, and thus this theme continues into the next chapter.
And consistent with that emphasis Paul reproves the Corinthians for acting just the opposite of showing the Lord's death by how they treated its members for whom Christ died: Declaring that even though they came together for the purpose of eating the Lord's super, and were indeed eating under that presumption, yet they were not acting eating the Lord's supper, because they were acting completely contrary to what the Lord's death meant by mistreating members bought by His blood, thus not showing unity with Christ and each other, but treating members as if they were spiritually unclean:
Now in this that I declare unto you I praise you not, that ye come together not for the better, but for the worse. For first of all, when ye come together in the church, I hear that there be divisions among you; and I partly believe it. For there must be also heresies among you, that they which are approved may be made manifest among you. When ye come together therefore into one place, this is not to eat the Lord’s supper. For in eating every one taketh before other his own supper: and one is hungry, and another is drunken. What? have ye not houses to eat and to drink in? or despise ye the church of God, and shame them that have not? What shall I say to you? shall I praise you in this? I praise you not. (1 Corinthians 11:17-22)
Therefore the apostle re-minds of the Lord's institution of that memorial meal and its purpose,
For I have received of the Lord that which also I delivered unto you, That the Lord Jesus the same night in which he was betrayed took bread: And when he had given thanks, he brake it, and said, Take, eat: this is my body, which is broken for you: this do in remembrance of me. After the same manner also he took the cup, when he had supped, saying, This cup is the new testament in my blood: this do ye, as oft as ye drink it, in remembrance of me. (1 Corinthians 11:23-25)
Paul (by the Spirit of Christ) then adds,
For as often as ye eat this bread, and drink this cup, ye do shew the Lord’s death till he come. Wherefore whosoever shall eat this bread, and drink this cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord. But let a man examine himself, and so let him eat of that bread, and drink of that cup. For he that eateth and drinketh unworthily, eateth and drinketh damnation to himself, not discerning the Lord’s body. (1 Corinthians 11:26-29)
It is not the nature of the bread and the cup that is the focus, but the purpose of the meal, which is to show (kataggellō: to proclaim, promulgate: - declare, preach, etc.) the Lord's death, which again is by sharing food with other members bought His the Lord's sinless shed blood. And thus to treat other holy members of that body as if they were outcasts was to not recognize the Lord's body, which Paul here refers to as the church he used to persecute.
Thus in the previous chapter the church is called "one bread, and one body: for we are all partakers of that one bread," (1 Corinthians 10:17) thereby showing communion/fellowship with Christ and each other, just like pagans have fellowship with demons by taking part in their dedicatory feasts, as would Christians if they took part in them:
Behold Israel after the flesh: are not they which eat of the sacrifices partakers of the altar? What say I then? that the idol is any thing, or that which is offered in sacrifice to idols is any thing? But I say, that the things which the Gentiles sacrifice, they sacrifice to devils, and not to God: and I would not that ye should have fellowship with devils. Ye cannot drink the cup of the Lord, and the cup of devils: ye cannot be partakers of the Lord’s table, and of the table of devils. (1 Corinthians 10:18-21)
Again, to take part in such feasts is to have fellowship with the object of the dedicatory feasts, but which was not be literally consuming the flesh and blood of them, while to act contrary to the Lord's death and its purpose, by mistreating holy members of it, is to not actually eat the Lord's supper and have and signify fellowship with Christ and each other.
And as that was the sin being reproved in 1 Co. 11:17-34, of some eating separately in lust for food, and ignoring others to their shame who were given nothing, then the solution was for members to examine their spiritual condition in the light of this, and as a practical measure, not come hungry to the Lord;'s supper, and be driven by hunger so as to treat it as if satisfying oneself with food itself was the purpose.
Wherefore, my brethren, when ye come together to eat, tarry one for another. And if any man hunger, let him eat at home; that ye come not together unto condemnation. And the rest will I set in order when I come. (1 Corinthians 11:33-34)
And as the body of Christ as the church (for whom Christ died) was the subject, then in the next chapter that theme continues.