Plausible-sounding Handwavium:

In the novel The Mote is God's Eye, aliens are trapped on their home world, even though there's a wormhole to another star. The wormhole opens INSIDE the other star, and the alien's shields grow the more energy they're exposed to. Their ships arrive at the star, the shields grow exponentially until they overload, and BAM. Human shields can't absorb energy, so they fly to the wormhole with a shield strong enough to keep out the star's energy. No bam.

I don't know what kind of handwavium tech is available in your world, but here's my suggestion. A shield that powers itself by absorbing energy exists. It doesn't have to be the normal thing (maybe it burns itself out in seconds and isn't useful for real-world applications, or they have a broken one that works this way).

Second, whatever FTL you have needs more power to go further, and to make the FTL field bigger. They have access to a large derelict ship with a jump drive, and install a self-charging shield into it. The whole thing is rigged to feed the power from the shield into the jump drive and expand the field size to a truly vast size. There can be dramatic short-cuts (like a 'bad' jump shifts things into parallel/alternate universes, or disperses mass across the galaxy - whatever) but the goal here is to shift enough mass of the star elsewhere so it is either gone or goes out.

No one uses this for any practical reason. Trying to power a jump this way will (at best) teleport you halfway across the universe to a random location. Only for your band of star-saboteurs, the more random the better.

Plausible-sounding Handwavium:

I'm not sure if there IS a good science-based answer to this, so here's as close as I can get.

In the novel The Mote is God's Eye, aliens are trapped on their home world, even though there's a wormhole to another star. The wormhole opens INSIDE the other star, and the alien's shields grow the more energy they're exposed to. Their ships arrive at the star, the shields grow exponentially until they overload, and BAM. Human shields can't absorb energy, so they fly to the wormhole with a shield strong enough to keep out the star's energy. No bam.

I don't know what kind of handwavium tech is available in your world, but here's my suggestion. A shield that powers itself by absorbing energy exists. It doesn't have to be the normal thing (maybe it burns itself out in seconds and isn't useful for real-world applications, or they have a broken one that works this way).

Second, whatever FTL you have needs more power to go further, and to make the FTL field bigger. They have access to a large derelict ship with a jump drive, and install a self-charging shield into it. The whole thing is rigged to feed the power from the shield into the jump drive and expand the field size to a truly vast size. There can be dramatic short-cuts (like a 'bad' jump shifts things into parallel/alternate universes, or disperses mass across the galaxy - whatever) but the goal here is to shift enough mass of the star elsewhere so it is either gone or goes out.

No one uses this for any practical reason. Trying to power a jump this way will (at best) teleport you halfway across the universe to a random location. Only for your band of star-saboteurs, the more random the better.