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We reveal a new statistical variability phenomenon in bulk n-channel metal-oxide-semiconductor field-effect transistors scaled down to 18-nm physical gate length. Rare but dramatic on-current degradation is observed in 3-D simulations of large ensembles of transistors that are subject to random dopant fluctuations. Physically, it originates from the random compensation of donors (from the source or drain extension) and acceptors (from halo implants) around the access regions to the channel, leading to mobile charge starvation, dramatic increase in the access resistance, and corresponding current collapse. The estimated frequency of occurrence of the phenomenon is higher than one in a hundred for a square device and higher than 10-4 for two-times-wider devices, as demonstrated by simulations of 10 000-device ensembles.