Will a neutron star always collapse into a black hole in the future? If a star has a mass greater than the Chandrasekhar limit, will it definitely become a black hole in the future or does it need to satisfy additional conditions?  Let me explain. Suppose the collapse of a star happens via the formation of the intermediate neutron star stage. Is it possible that the neutron star remains stable forever and stops evolving into a black hole in the future?
 A: The Chandrasekhar mass is a (nominal) upper limit for the mass of a white dwarf supported by ideal electron degeneracy pressure. It is about 1.4 solar masses for most plausible white dwarf compositions.
In reality, white dwarfs that are a little below this limit will either collapse or explode. Which happens depends very sensitively on the detailed composition of the white dwarf, how it accumulates the additional mass and the uncertain physics of pycnonuclear reactions in dense materials.
If the white dwarf collapses it is likely to form a stable neutron star. The maximum mass of a neutron star is somewhere between 2 and 3 solar masses and so much larger than the Chandrasekhar mass.
If the neutron star does not accumulate further mass then there is no reason why it cannot remain as a stable object.
NB: I am talking about stable on timescales of many billions of years and ignoring possibilities like proton decay that might occur on much longer timescales.
A: An isolated neutron star with a mass below the maximum mass of a neutron star$^\star$ is stable and won't collapse into a black hole. Since it is held together by degeneracy pressure, it isn't burning fuel so isn't going to "run out" of pressure.
A neutron star that is accreting matter or that merges with another neutron star, can form a black hole, if it accumulates enough mass that it is no longer stable.

$^\star$ Originally I wrote "Chandrasekhar limit", but as pointed out by @ProfRob while this applies to white dwarves, for neutron stars the maximum mass is not simple to calculate and depends on the equation of state of the neutron star. However, there is some maximum mass that can be supported.
A: Terminology note: the Chandrasekhar limit $M_C \approx 1.4 M_\text{sun}$ is for electron-degenerate matter. The analogous limit for neutron-degenerate matter, $M_\text{TOV} \sim 2.5 M_\text{sun}$, is named for Tolman, Oppenheimer, and Volkoff. We have much less confidence in our estimate for the TOV limit than we do in the Chandrasekhar limit, because we know less about the equation of state for neutron-degenerate matter than we do for electron-degenerate matter.
We are aware of several stable neutron stars with masses $M_C < M_\text{object}$; there’s a partial list in Wikipedia article linked above.  But I suspect you were asking about the stability of neutron stars with masses above $M_\text{TOV}$.
There is speculation in the literature about the possible existence of quark stars, in which the nucleon degrees of freedom dissolve and the star is supported by degeneracy pressure among the free quarks.  It’s possible in principle that a neutron star which accumulated mass beyond $M_\text{TOV}$ could collapse to a quark star, analogous to the collapse of a white dwarf (or of an electron-degenerate stellar core) to a neutron star.  But we know even less about the equation of state for quark matter than we know for neutron matter. I don’t think it’s known for certain that the mass limit for a quark star is any larger than the mass limit for a neutron star. It’s also unknown whether quark stars would consist of up and down quarks, like normal baryonic matter, or whether the phase transition would produce a substantial fraction of strange quarks.
The Wikipedia page lists a number of (unconfirmed) quark star candidates, and describes why confirmation is so difficult.  It may well be the case that quark stars don’t exist, and that an overmassive neutron star is definitely doomed to become a black hole.
The neutron-star merger event GW170817 produced an object with final mass $2.74^{+0.04}_{-0.01}M_\text{sun}$. That gravitational-wave event suggested the new object collapsed to a black hole on a timescale of a few seconds (as opposed to milliseconds, or hours). If you’re interested in the nitty-gritty details of black hole formation from “supermassive neutron stars,” that would be a path into the literature.
A: For this question, we are not completely sure if it will become a black hole. Worst case scenario is that the neutron star is very unlucky and never meets another atom every again. Then, it will slowly decay, similar to Hawking radiation, and to Quantum Tunneling. Moreover, light can also escape neutron stars, and as light is a small piece of energy, not only neutron stars stay put, gradually they will disappear too.
Note: Neutron stars will cool off and become dark after a very long time. However, quantum decay and 'Hawking Radiation' will still remain.
