I know people who work as consultants and make $10K-$25K in a month. To these people, the YC 'investment' is more of a deterrent. The main attraction would be to get wired into the network and tap into the experience YC and its alumni can offer. It would be good if you could clarify whether it makes sense for them to apply or not.
Pretty sure the official answer is that they wouldn't be interested in taking someone who could only work part-time. I'm sure there are edge cases here and there, and YC is all for creative ways to stay alive financially (AirBnB sold cereal to stay alive - http://money.cnn.com/galleries/2010/smallbusiness/1003/galle...), but the YC school of thought is that a startup should occupy 100% of your work-related effort.
Of course, plenty of us worked as consultants for $10K-$25K/month before YC (er, closer to $10K) in order to build up some savings to live on.