One major concern of existing wireless localization systems is the identification of nonline-of-sight (NLOS) signal propagation, since NLOS can be considered the dominant source of localization error. Present identification methods usually assume that NLOS could make it not possible to perform localization in a consistent manner. However, the validity of the foregoing assumption has not been properly investigated. This paper presents a theoretical analysis of mobile user localization involving one or more NLOS beacons and shows the given assumption as being invalid when the estimated user location is outside the convex hull of the beacons used in the localization. It also proposes an efficient algorithm for checking whether the estimated location of a mobile user is inside the convex-hull region in both 2-D and 3-D space. Extensive localization experiments on different wireless networks demonstrate that using current NLOS identification methods and classical localization algorithms could yield localization results with grossly underestimated errors.