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You're observing a massive object (probably a neutron star), and it is moving at a significant fraction of the speed of light relative to you. The mass of the object is just below the mass necessary to form a black hole of the corresponding size (ie, if a relatively small amount of mass was added, or the current mass was compressed, it would form a black hole). In the moving reference frame of the object, it is not observed to be a black hole, and it doesn't have sufficient density to form one.
The interesting conundrum is that from your point of view, the object undergoes length contraction. In this case, if an object of the same mass were to have the size that you're observing due to length contraction, it would be of sufficient density to form a black hole. Obviously, you don't observe the moving object becoming a black hole, because it isn't actually doing that, but you observe what appears to be an object of sufficient density to become a black hole, but is not a black hole.
What makes this possible? Is the observed mass from your reference frame different for some reason? Does what you observe not matter? Is it something else?