In the Wikipedia article about stellar engineering, I found this quote:
In The Saga of the Seven Suns, by Kevin J. Anderson, humans are able to convert gas giant planets into stars through the use of a "Klikiss Torch". This device creates a wormhole between two points in space, allowing a neutron star to be dropped into the planet and ignite stellar nuclear fusion.
Now this is definitely impossible, as neutron stars are degenerate and cannot fuse. But what if we dropped a helium white dwarf or extract the hydrogen-burning core of a low-mass star and put it into a large gas giant or non-fusing brown dwarf? Would this trigger fusion or would this fail as well (presumably because the white dwarf is also degenerate)?