I have read a little about quark stars (found inside neutron stars) and wonder if the process could go deeper. In a quark star the idea is that the pressure is so much that all matter breaks down into quarks. This would be denser then a neutron star normally would but not as dense as a black hole. Neutron stars need to be fairly large, for a neutron star, to accomplish this.

Saying this could the understanding of a black hole be compared to this as in the idea that matter and even quarks are broken down even further creating a star comprised of string (strings coming from the String theory or TOE idea)

I did not know of them - quick search gave:

"Neutron stars are the dense cinders of massive stars which have gone supernova and crushed the matter in their cores to densities of 10^14 grams/cc. At these densities, equal to that of nuclear matter, most of the protons and electrons have combined to create neutrons, so that the core is nearly 100% pure neutrons. The cinder is prevented from further gravitational collapse because neutrons are particles with 1/2-unit of quantum spin, and only two of these can exist in the same quantum state. This produces what is called Fermi Degeneracy Pressure which at these densities and neutron star masses, can be as strong as gravity, but a repulsive force.
Neutrons are composed of three quarks, which are also capable of generating the same kind of degeneracy pressure, but first you have to compress the neutron star to densities of 10^16 grams/cc or higher. This requires an amount of mass in the neutron star that puts it nearly at the black hole limit for its size...about 25 kilometers in radius or less. At these densities, the neutrons in the core of this object begin to dissolve into their constituent quarks, and so in the deep interior of the cinder you end up with a 'gas' of quarks. As you continue to crank up the density even higher, the quark-state encompasses more and more of the neutron star. The problem is that such 'quark stars' are nearly the same size as the black hole limit for the amount of mass and size, so when you factor-in the relativistic effects, quark stars are probably a very unstable and fleeting phase in the life of a very massive neutron star. "

From www.astronomycafe.net/qadir/ask/a11795.html

Thus in answer to your question (does it go further?) - I think not as (1) quarks are now considered to be the fundamentals (I think, not stings) & (2) if the "quark core" even exists it seems to be only a stage on the way to becoming a black hole. - see last text above.

I don't believe there is evidence at this point that quarks can be broken down further. So, you may be talking about the same thing. Different quarks = strings vibrating at different frequencies.

More recent theory suggests that the quarks, once 'liberated', are able to arrange themselves as up/down/strange quarks, and convert the 'neutron star' into a single large 'atom' referred to as 'strange matter'. Lots of good information on 'strangematter' and 'strangelets' via Google. The LHC might be capable of creating strangelets.

Strings are a fairly new thought. If you were to search for therory of everything or string theory you would find them. The are hoped to be the thing that brings quantum mechanics and the theory of reletivity together.

"Astronomers recently announced that they have found a novel explanation for a rare type of super-luminous stellar explosion that may have produced a new type of object known as a quark star."

Read more (http://yubanet.com/scitech/Not-a-Quirk-But-a-Quark-a-Quark-Star.php)

Quark stars are black holes. They also contain electrons. A neutron star has an escape velocity of 2/3 light speed, yet neutrons survive! Quarks and electrons are elementary particles and I think it would take far more than a black hole to destroy them.

I would think if you could crush matter into strings, you would no longer have matter of any kind and so no longer have the cohesive gravity to make a single mass.

From the report I tend more to a dense star stealing lots of hydrogen from a companion star and when it went super-nova, the hydrogen layer it had built up on it's surface above it's shell of heavy elements then ignited too.