Do you think the sun will shut off like a lamp, or just burn out, gradually. In order for a huge ball of fire, such as the sun, to instantly go out, there'd have to be a block of ice floating around the universe that's about 500 times the size of the sun.
If plants did die off, slowly or instantly, our species is so complex that it has the ability to evolve. Many would die, many would stay alive with machines, survivors will evolve. They find that Life can exist under the most extreme conditions, such as the surface of Titan.

And, besides, without the sun, we still have our oceans.