As others have pointed out, the reason why we don't see non-stellar neutron stars is that the pressures needed to form them are usually only found in stars. Lower pressures don't form neutron degenerate matter and higher pressures form black holes.
I think part of your question may be whether or not smaller quantities of neutron-degenerate matter, which would be under lower constant pressure, are stable. I think the answer is either "no" or "not very much lower pressure", since even the crusts of neutron stars are believed to have separate nuclei: https://link.springer.com/article/10.12942/lrr-2008-10 . In small quantities, neutron-degenerate-matter would probably explode with extreme force, as if were just a ridiculously superheavy and super-neutron-rich atom: https://physics.stackexchange.com/questions/10052/what-would-happen-to-a-teaspoon-of-neutron-star-material-if-released-on-earth
However, some theories suggest that this would not be true for denser types of quark-gluon matter that are likely to be found inside massive "neutron stars". The concept of "strange matter" made of up, down, and strange quarks is well known, and it is has been famously predicted by some to be stable at room temperature, after it has been formed, perhaps even converting normal matter it touches into strange matter (or, alternatively, maybe not). "Strangelets", or tiny pieces of strange matter, are one candidate for what dark matter could be, and it has even been suggested that they might hit Earth about once a year and explain some weird craters: https://arxiv.org/ftp/arxiv/papers/2007/2007.04826.pdf
Similarly, it has also been suggested that very heavy atomic nuclei (A>about 300), may collapse into a sea of up and down quarks called "up-down quark matter" or udQM, which might actually be more stable than "strange matter" (uds-matter). This has been suggested to create a "continent of stability", where nuclei this big are actually stable, unlike smaller superheavy nuclei, and has been suggested as an alternative to strangelets as a dark matter candidate: https://en.wikipedia.org/wiki/Continent_of_stability
Needless to say, both of the types of QCD-matter are extremely theoretical because A) only supernova-like pressures can create them, even if they do turn out to be stable or metastable at low pressure, B) our methods of making superheavy nuclei with particle accelerators have not progressed that far yet, C) the proper quantum-chromodynamics calculations are very difficult to do, and really good calculations of this sort have only been done for small nuclei, so the math these predictions (including the one about neutron-degenerate matter) are based on is all approximations that probably introduce significant errors.
It is possible that further investigations of neutron-star collisions will reveal more about the nature of their interiors, and whether these collisions might even be able to liberate some ultradense matter without it decaying into normal-sized nuclei. (If it doesn't, that doesn't mean this ultradense matter couldn't be stable, since it could just be the energy of the collision that destroyed it, and even if it does, such a source is not likely to be a major source of dark matter, because that would result in the amount of dark matter increasing as the universe aged, which I think goes against observation.)