Unless I am mistaken (and I very well could be), it has never been a requirement for the faithful to receive from the cup. It is however a requirement for the clergy.
Receving under one species is complete and sufficient, as we receive Jesus’, body, blood, soul and divinity.
I hate to use such a crude example, but here goes.
If you buy a steak at the grocery store, it is the body of the cow. The meat is still red because there is still a certain amount of blood in the tissue itself. Have you ever noticed that when meat sits for a while, blood still comes out of it? That same steak will lose the blood in the tissues over time, and turn brownish in color.
So, in looking at the Eucharist being the Body of Christ, there is still blood in the body.