That theory is half right, compared to the theory I believe.
I do believe the big bang or, to be specific, an origin of the universe where everything was together on one place of unknown size/density. Then, for whatever reason, it expanded/exploded. Finally, we expand to where we are now.
The universe is a cone shape, originating from where the big bang happened (I'll call it the origin). It is constantly expanding (proven fact). Stars burn out, and new stars are created (fact), but we eventually will run out of material to make stars (law of physics, matter cannot be created or destroyed). So, eventually all of the stars will burn out and we will not have the most important part of life: light.
Why is light so important to life you say? Well, that would be because every living organism is either an
autotroph or
heterotroph. Basically, a heterotroph will eat the autotroph for use in creating
adenosine triphosphate (ATP), our body's source of energy. A huge part of ATP is the carbon. Autotrophs create ATP by taking in carbon dioxide and heat (from
photosynthesis -- the important part for my point) for the carbons needed (I'm not going to describe the cycle, it takes too long). Heterotrophs use that carbon that is taken in and used by the autotrophs for their own cycle, which creates ATP. Of course that's a very, very, very simplified explanation, but what it boils down to is that life depends on light through photosynthesis to create ATP (energy we can use).
So, once all of the stars burn out, life will end. For sure. It will take billions upon billions of years, and we can actually calculate this number if we ever knew how much material it took to create a star, or where all of that necessary material is; by that time we will be either extinct or posses the technology necessary to, literally, create our own star and planet, because that's what it will take to save life in the long run. Time will always be there, but not us.