In earlier times, contact lenses break in your eye could prove a serious hazard because they were made from glass. Nowadays modern contacts are made from better material. Hard contacts and soft contacts are two type s pf contacts. It's difficult for hard contacts to break or crack. Only enough force can break the lens, if so, the strike itself would be much more of a concern. While modern soft contact lenses can tear, but rarely cause damage to the eye. So you should remove broken contact lenses at once. www.ehow.com is a site that introduce many ways to deal with broken contact lenses in eye.
It is so dangerous for the eyes when the contact lenses are broken in your eyes. You'd better get the broken contact lenses out of the eyes. Or else, the broken contact lenses may hurt your corneal. And your eyes may feel dry if you wear the broken contact lenses for a long time in your eyes.
Well, as far as I know, despite that the possibility is quite low, however, I have once got that bad thing happen to me. Of course, there will be tremendous likelihood that your eyes might be scratched by the broken pieces, even bloodshed. But actually, if the quality of your contacts are quite good, there will be no danger. My advice for you is to wear short term contacts, rather than those with long duration.