This has been a verse that I have misunderstood all my life. I have always understood this to mean the common meal. In other words, if a brother was a fornicator, I understood it to mean that I could not eat a common meal (breakfast, dinner or supper) with that person.
"But now I have written unto you not to keep company, if any man that is called a brother be a fornicator, or covetous, or an idolater, or a railer, or a drunkard, or an extortioner; with such an one no not to eat." 1 Corinthians 5:11 KJV
However I have come to realize there is a much bigger issue at stake in this text. It is not speaking of the common meal; it is speaking of the covenant (Lord's supper) meal. It is not speaking of the common table; it is speaking of the communion table.
The first reason this must be true is the context is dealing with public church discipline when the church gathers together (1 Corinthians 5:3-5; Matthew 18:18-20).
The second reason is the context of "eat." What is eating in the context of 1 Corinthians 5? Is it the common meal or the covenant meal. I believe the context will prove that it is the covenantal and sacramental meal of the Lord's Table.
If we can settle what the feast of verse 8 is, we can settle what the eat of verse 11 is. On is forced to accept that eat in verse 11 refers to the feast in verse 8. I believe that feast is the Lord's Supper.
"Purge out therefore the old leaven, that ye may be a new lump, as ye are unleavened. For even Christ our passover is sacrificed for us: 8 Therefore let us keep the feast, not with old leaven, neither with the leaven of malice and wickedness; but with the unleavened bread of sincerity and truth." 1 Corinthians 5:7-8 KJV
The feast that we are to keep is the one that memorializes the sacrifice of Christ on our behalf. What feast does this? The Lord's Supper and the Lord's table is the only event and place that can possibly do this. In my opinion, since the feast seems to be the Lord's Supper, the command "with such a one not to eat" refers to the same.
There are a number of problems that we encounter if this refers to a common meal. If you want to discuss these then comment and I will be glad to.