Concerning manners piece there is an old story about the last piece of chicken one evening. A wind came up and blew out the kerosene lamps. A scream was heard. When the lamps were re-lit, there was grandpa holding the piece of chicken with four forks in the back of his hand. 
Emmett
Funny story Emmett! Hadn't heard that one.
Back in Wisconsin we used to call the last remaining piece of food "the orphan." Of course, someone almost always "adopted" it to save the cook the trouble of wrapping and storing it.
These days (here in Arizona), that scenario seems to only play out during halftime at our poker games, when my wife brings in a platter of pizza for the gang. In most cases, 2-3 people will cut the cards to see who gets the last piece. If everyone is too full, the dog gets it. And of course, the dog has no issues with taking that last piece. Hell, she'll take a piece off your plate if you don't watch her. 
I grew up calling the last serving or morsel the "Old Maid," as Martha points out. In my understanding, it was not from the idea that the piece itself was left behind as the "Old Maid," but rather that the person who dared take that piece would be cursed to be an "Old Maid." Either way, in my family the morsel itself was known as the "Old Maid."
In a quick internet search, I also find the phrase "thrive bit."
To me, "old maid" in a food context refers to unpopped kernels of popcorn.
Heimhenge said:
Funny story Emmett! Hadn't heard that one. ...
Heimhenge, you may have encouraged me too much. Here is a conversion to a six-word story (my first):
"Mannersbit. Dark. Scream. Forks in hand."
Out of context, it might not be very good.
Emmett