The implication arising from the closing words of the Isaiah 28:16 quote is that those who do not believe will be “put to shame,” dishonoured. To show the extent of the shame they receive, Peter quotes Psalm 118:22, with its embarrassing (for the unbelievers) reference to God's elevating to the position of cornerstone the very stone the unbelieving builders had rejected.
7 So the honor is for you who believe, but for those who do not believe, “The stone that the builders rejected has become the cornerstone,”