At the session I run we have a number of very good unaccompanied singers and one chap who used to bury his face in a lyrics sheet, throw the tune out of the window and generally was in dire need of some friendly advice so he could improve and feel better about what he was trying to achieve (as well as not becoming the loo/bar/cigarette break performer in the circle!)
One of our veteran singers did just this in a very tactful and supportive manner and the chap never came back!!
As an open session, unlike a folk club or spot singers you have little or no quality control!
It is a tricky issue really as you don't want to utterly discourage someone even if they are painful to listen to but some people can take any criticism however well meaning completely to heart even though saying 'yeah that was great!' would be an utter lie - i think it's about finding the middle ground and trying to be tactful about it.
I'll always praise those in the session who really stand out with a great performance, otherwise everyone no matter what quality does get a clap for at least trying.
I was probably bloody awful when I started out so I'd hate to think those who can improve and are learning would be put off but then there are always a few hopeless cases too.....!