The substructures of light bosonic (axion-like) dark matter may condense into compact Bose stars. We study collapses of the critical-mass stars caused by attractive self-interaction of the axion-like particles and find that these processes proceed in an unexpected universal way. First, nonlinear self-similar evolution (called "wave collapse" in condensed matter physics) forces the particles to fall into the star center. Second, interactions in the dense center create an outgoing stream of mildly relativistic particles which carries away an essential part of the star mass. The collapse stops when the star remnant is no longer able to support the self-similar infall feeding the collisions. We shortly discuss possible astrophysical and cosmological implications of these phenomena.
