What if the only light provided to a plant was from the green spectrum would plants adapt or starve?
Green is pretty much the last color that you'd want for a plant. Thinking logically, a plant is green because it reflects green light, and hence, plants do not absorb green light for photosynthesis.
Let's take a look at the spectral absorbance of the various pigments in plants:
You can see that all the pigments show very very poor absorption when it comes to green. Plants tend to absorb light at violet, blue, and at red colors predominantly.
To answer your second question: what would happen if the sun spectrum changed to green?
For all the "what if" questions, we cannot give a definitive answer, and all of what I say will be purely speculations. Let's see what could actually happen:
Possibility 1: Plants will evolve to develop different pigments that absorb wavelengths that correspond to green light. Since the sun itself is green, and hence the entire surroundings will be green. Plants absorb all of the light that the sun is capable of absorbing, and hence will appear to be black to the human eye.
Possibility 2: Plants will die out, due to the sudden change in the sun's spectrum, which will cause the rest of the life forms that depend on plants to die out as well.