Question

As stars give off energy,do they lose mass

Answer 1

I would say yes, they convert mass into energy; and the energy slowly fades away in different forms of light.

Answer 2

Yes! The energy they give off have an equivalent mass, and this mass is lost to the star. This follows from (a) the equivalence between mass and energy, and (b) conservation of mass. As an example, our Sun, which gives off tremendous amounts of light, loses 4 million tonnes a second, just through the light that leaves the Sun - that is, apart from any solar wind.

Hope this helps!