  Astrophysical black hole candidates, although long thought to have a horizon,
could be horizonless ultra-compact objects. This intriguing possibility is
motivated by the black hole information paradox and a plausible fundamental
connection with quantum gravity. Asymptotically free quadratic gravity is
considered here as the UV completion of general relativity. A classical theory
that captures its main features is used to search for solutions as sourced by
matter. We find that sufficiently dense matter produces a novel horizonless
configuration, the 2-2-hole, which closely matches the exterior Schwarzschild
solution down to about a Planck proper length of the would-be horizon. The
2-2-hole is characterized by an interior with a shrinking volume and a
seemingly innocuous timelike curvature singularity. The interior also has a
novel scaling behavior with respect to the physical mass of the 2-2-hole. This
leads to an extremely deep gravitational potential in which particles get
efficiently trapped via collisions. As a generic static solution, the 2-2-hole
may then be the nearly black endpoint of gravitational collapse. There is a
considerable time delay for external probes of the 2-2-hole interior, and this
determines the spacing of echoes in a post-merger gravitational wave signal.
