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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. In this talk I will consider the asymptotically free quadratic gravity as the UV completion of general relativity. Using a classical theory that captures its main features, we find that sufficiently dense matter produces a novel horizonless solution, the 2-2-hole. It closely matches the exterior Schwarzschild solution down to about a Planck proper length of the would-be horizon. I will describe interesting features of the 2-2-hole and various physical implications. As a generic static solution, the 2-2-hole may be the nearly black endpoint of gravitational collapse.