The solar wind contributes a very small amount of matter to the gas giants. As the sun approaches the red giant phase, the solar wind increases significantly. 10% of the sun's mass lost as solar wind over its lifetime, which is equal to 100 Jupiters in mass. After the red giant phase the sun releases the outer, mostly hydrogen, outer layer in the form of the planetary nebula. The planetary nebula is about 50% of the mass of the sun, which is equal to 500 Jupiters in mass, the remaining 40% of the sun will be left as the white dwarf.
After all this additional mass, most of which is hydrogen, is added to the gas giants how massive would they be and would any of them reach brown or red dwarf status?
Smallest brown dwarf is 13 Jupiters in mass, which is able to fuse deuterium. Smallest red dwarf is at 75 Jupiters in mass, which can fuse hydrogen.