Is it possible that two neutrons can merge? At the center of neutron stars are tightly packed neutrons with almost no space between them. Also, proton and electron have all merged (electron capture) forming as much neutrons as possible. When this star exceeds the Tolman–Oppenheimer–Volkoff limit, the result would be a black hole.
Out of curiosity, if neutrons in extreme sense could ever merge or undergo a $n+n$ reaction?
 A: Wikipedia says:

The dineutron, containing two neutrons, was unambiguously observed in
2012 in the decay of beryllium-16.[8][9] It is not a bound particle,
but had been proposed as an extremely short-lived resonance state
produced by nuclear reactions involving tritium.

It references this article, “First Observation of Ground State Dineutron Decay: 16Be”.
A: As far as I understand, the nuclear force has a potential curve that looks similar to the Van Der Waal forces. Notice how the potential goes up exponentially when nucleon separation is approaching zero.

So even if neutrons are neutral and there is no Coulomb repulsion, you will have to overcome the nuclear force for merging two neutrons, which is extremely difficult to do.
A: The existence of quark stars has been considered. These are hypothesized to be more dense than neutron stars and to consist of quark-gluon plasma. In such a plasma the boundaries between nucleons would no longer exist. Many open questions exist about quark matter, but the existence quark-gluon plasma is considered to be confirmed.

