We search broad solar neighborhood for K- and early M-type dwarf stars with greater than Galactic escape velocities based on Gaia DR3 proper-motion and distance data exclusively. We find 11 bona fide hypervelocity star candidates, which have total velocities 500 km/s relative to the Galactic center computed both with trigonometric-parallax based and photometric distances.
Zhuiko et al. (Mon,) studied this question.