ADDENDUM: In response to @Frostfyres comment below, here is the idea summarized: Add large quantity of fissile element to star in hopes of prolonging its life. The result is other than is intended.
ADDENDUM 2: From the comment, @Douglas looked the linked question from the astronomy stack and took away that the answer was "No". The answer there is actually "Maybe". Below is the relevant text copied from that answer. .
If you have a material inside that slows the reaction, absorbs and
re-admits Neutrons you could probobly generate a sustained burn -
similar to what happens inside a nuclear plant while maintaining
enough gravity to keep the object in one piece and over time, That
would heat up and glow like a star in time and last for a while.
In my answer the dwarf describes that this, in their pride, is what the dwarves tried to do. As regards "completely unrelated" I would plead it is not complete: the answer includes a dwarf, and a star.
ADDENDUM 3 From @MozerShmozer's comment. The link is about a large mass of fissile material. Q:Could it act like a star? A:Maybe it could. OP: The dwarves have a fusion star. They screw it up. How? My answer: With their skill they build it a fission heart, like the thing described in the link. They put it in their fusion star. It is classic hubris: supreme technological skill versus the inevitability of death. This makes for a good story because as in other cases when science opposes death, the dwarves do not need to screw up or blunder. They can be correct in their estimation of their skill, succeed in their attempt and then be horrified at the result.
It is ironic that I thought this was such a cool scifi answer, but failed so hard to convey it to an audience I thought would be right there with it. I will keep the day job.
“We knew that soon Grandfather would die, and burst. When he ran out of the light stuff that drives him.”
Tys watched the dwarf roll something between his fingers as he spoke – a well worn piece of some machine, she guessed. It shone like nickel. “You call your sun Grandfather?”
He nodded, the nickel piece clicking against his rings. “Because we love him, and we hide from him. And we knew he would die. We thought of a way to help him.” The dwarf flipped up the bit of metal and quickly used it to deeply scratch a perfect circle in the table top, dividing it neatly into pie shaped tenths. He blew the scratched pieces of table away and then set the metal bit down in one section. “Fusion happens only with the light stuff – the starstuff.”. He looked at the circle and back at Tys, apparently thinking that this scratching would serve as some sort of visual aid.
Tys nodded. The pie on the table did not mean much, except that they should cover it with a placemat before they left. But she did understand fusion.
The dwarf, satisfied, looked back down and rolled the metal bit over two pie slices. “When the light stuff is gone, he dies. Withers, or bursts. But we thought – could he live again, but in a different way?”. As he spoke, the dwarf looked past Tys' ear at something that was not there. “Like the ones who dive deep when they die, living in the dark tunnels on the glow of the earth?”
Tys looked at him quizzically. “Dive deep?”
He cut her off, his mind far away in a different place and time.. “We had long known the method to make energy from the heavy stuff – the fission. The second greatest energy. Some thought the first.” He moved the metal piece across the circle to rest in a different slice, and laid his thick finger beside it. “And then in space we found the burst heart of a star long dead, made only of the heavy stuff. More than any could use in a thousand thousand lifetimes. And we thought: if with our skill we could rebuild this dead heart and give it to Grandfather it could become his own heart. And in his grip that dead heart could come back to life with fission. He would gain a new youth. New life.”
The dwarf fell silent. “So?” asked Tys. “Did you give him the dead heart? Did it work?”
The dwarf scooped up the old metal piece, gripping it tightly in his palm. She could see the tendons stand up on the back of his hand. “Yes we did.” He looked at her bleakly. “And yes… it did.”