The carbon-rich WC5 star WR 114 was not detected during a 15.9 ksec XMM-Newton observation, implying an upper limit to the X-ray luminosity of L-X less than or similar to 2.5 x 10(30) erg s(-1) and to the X-ray to bolometric luminosity ratio of L-X/L(bo)l less than or similar to 4 x 10(-9). This confirms indications from earlier less sensitive measurements that there has been no convincing X-ray detection of any single WC star. This lack of detections is reinforced by XMM-Newton and Chandra observations of WC stars. Thus the conclusion has to be drawn that the stars with radiatively-driven stellar winds of this particular class are insignificant X-ray sources. We attribute this to photoelectronic absorption by the stellar wind. The high opacity of the metal-rich and dense winds from WC stars puts the radius of optical depth unity at hundreds or thousands of stellar radii for much of the X-ray band. We believe that the essential absence of hot plasma so far out in the wind exacerbated by the large distances and correspondingly high ISM column densities makes the WC stars too faint to be detectable with current technology. The result also applies to many WC stars in binary systems, of which only about 20% are identified X-ray sources, presumably due to colliding winds.