There was also the Tox Uthat, the MacGuffin from the third-season episode “Captain’s Holiday”, that could perform the same trick. No explanation is ever given as to how the device works, beyond the Treknobabble description of “quantum phase inhibitor”, so beyond “piece of alien technology from three centuries after TNG that works by Trek science rules”, there isn’t much room to speculate as to how it shuts down stellar fusion reactions.
In Star Trek Generations, the bad guys had a substance which could stop the fusion inside a star, making it collapse and produce a solar-system-obliterating shockwave. This is actually somewhat feasible compared to your average Star Trek science: for various reasons I don't think it could actually exist in the way it does in the movie, but you could conceive of a substance that acted as "fusion poison", producing more of itself when it collided with energetic hydrogen but was not itself able to be fused further. Even the bit about the shockwave was really plausible: it's pretty much exactly what happens in an actual core collapse supernova.
The one really unfeasible part was that it couldn't happen instantaneously like it did in the movie. Even in the core of starts, most hydrogen atom collisions don't result in fusion - they can't overcome the Coulomb barrier. If you introduced a self-replicating fusion poison into the core of the Sun, it would grow only very slowly, at least at first. You could imagine a fusion poison produced almost no notable effects for centuries or millennia, then maybe a one-lifetime period of noticeable effects, then the Sun went out and everyone died.
Which I actually think would be a better story. Suppose you knew that there was a fusion poison, but not exactly when the Sun would collapse, since astrophysical time scales are immense and imprecise. It's going to be in the next 10,000 years, but beyond that you're not certain. Would people try to escape the Solar System? What would life be look in an era of certain doom but highly-uncertain timing?