Frankly, most lay Catholics don't believe in the real presence.
John Calvin believed in the Real Presence, just not the words "flesh & blood" coupled along with it. That confirmed him a heretic in papal eyes.
He spoke of experiencing it, but not being able to properly describe it.
So I wonder. If he truly did partake of the essence of it, but had difficulty agreeing with the extent that the formulaic and fervently insisted upon orthodox/catholic wordings used to describe it, then how could he be so far wrong--- if the Lord Himself did indeed (by deep mystery?) did inhabit the offering?
http://theologytoday.ptsem.edu/jan1969/v25-4-bookreview7.htm
If it be in any way the flesh & blood, (mystical or no) after consecration, I do not believe that any form of "transubstantiation" or as Calvin perhaps put it(?) "substantially present" occurs without the sanctifying acceptance of believers, together in unison if at all possible, partaking of it.
Any left-overs can be utilized normally. That's what they did with the left-over bread in the earliest years of the church in Rome, isn't it? Took the left-overs home, distributed it to those who had need or could make use of it, and ate it like normal bread?
It wasn't sacrilege, then to dispose of the remaining ordinary parts of the bread or wine in such manner... Though there are ancient reports of various converts saying such as "I go to so-and-so's, the bread there is much better" etc., which hints at showing, that even wa-aay back, not all actually received, or in the least perceived or took note that they did, in their own spirit or soul.