Can black holes be a subset of quark stars? If not, what are black holes made of?
Black holes are not made of anything... at least nothing in our current understanding of reality.
We understand black holes in terms of General Relativity, the theory of gravity.  In this theory there are some &quot;vacuum solutions&quot;  These are solutions that have no matter at any point in spacetime.  One solution is &quot;flat space&quot;, but another solution is a solution with a singularity in time and space.  This solution was discovered by Schwatzchild, and for long was thought to be a mathematical curiosity but not physically real.
But it was later discovered that when a star collapses under gravity it reaches this state.  All the matter falls towards the singularity and we can't describe what happens later than the singularity in time. From the outside it seems as if all the mass of the star is concentrated at one point, but there is actually nothing inside, just the distorted spacetime.
In General relativity nothing can exist in a black hole. For anything falling beyond the event horizon, all directions lead to the singularity.  It is as unavoidable as &quot;next Wednesday&quot;. No ball of matter could exist. In normal space, two particles can remain separate. Inside a black hole this isn't possible, since both particles end up at the singularity in a finite (and short) amount of time.
Now we aren't certain if this truly describes reality, because we lack a theory of gravity that takes account of quantum mechanics. It might be that the singularity is real. It might be that something happens (with strings or something) that prevents the ultimate collapse to a singularity. Whatever it would be outside our current models of reality.  Not &quot;quarks&quot;.