The XQ-100 survey provides optical and near-infrared coverage of 36 blindly selected, intervening damped Lyman {alpha} systems (DLAs) at 2<z_abs_<4, simultaneously covering the MgII doublet at {lambda}{lambda}2796,2803{AA}, and the Ly{alpha} transition. Using the XQ-100 DLA sample, we investigate the completeness of selecting DLA absorbers based on their MgII rest-frame equivalent width (W_0_^2796^) at these redshifts. Of the 29 DLAs with clean Mg II profiles, we find that six (20 per cent of DLAs) have W_0_^2796^<0.6{AA}. The DLA incidence rate of W_0_^2796^<0.6{AA} absorbers is a factor of ~5 higher than what is seen in z~1 samples, indicating a potential evolution in the MgII properties of DLAs with redshift. All of the W_0_^2796^<0.6{AA} DLAs have low metallicities (-2.5<[M/H]<-1.7), small velocity widths (v_90_<50km/s), and tend to have relatively low N(HI). We demonstrate that the exclusion of these low W_0_^2796^ DLAs results in a higher mean N(HI) which in turn leads to an ~7 per cent increase in the cosmological gas density of HI of DLAs at 2<z_abs_<4; and that this exclusion has a minimal effect on the HI-weighted mean metallicity.