We investigate energy dissipation and the distribution of particle velocities at the jamming transition for overdamped shear-driven frictionless disks in two dimensions at zero temperature. We find that the dissipation is caused by the fastest particles and that the fraction of particles responsible for the dissipation decreases towards zero as jamming is approached. These particles belong to an algebraic tail of the velocity distribution that approaches similar to v(-3) as jamming is approached. We further find that different measures of the velocity diverge differently, which means that concepts such as typical velocity may no longer be used, a finding that should have implications for analytical approaches to shear-driven jamming.