The ISS has a limited lifetime. They think it will last beyond 2020 which is well beyond the original design life of some of the components. But eventually it will degrade to the point there it is no longer usable.
It is difficult to repair spaceships in orbit. At least with present day technology. They plan to just do a controlled de-orbit so that it burns up in the atmosphere. Because of its low orbit it needs periodic boosts to prevent it entering the Earth's atmosphere and de-orbiting naturally. So you can't just leave it there when it is no longer habitable, but have to de-orbit it, or do something with its components.
Some of the modules might still be usable at that point and if so they might disassemble it and use the still useful modules for another space station.
The Russians are committed to the ISS until 2024, but have talked about possibly detaching the Russian modules in 2024 and using them to make a new Russian space station in LEO. This article is from 5th March 2015, so reasonably up to date. I suppose this depends on how things develop between Russia and the other ISS partners politically in the future. NASA Making Plans for Russia's Secession From ISS
As to whether it could double as a spaceship - not with present day technology - not easily. But - if we had enough fuel to do it - e.g. abundant low cost fuel supplied to LEO - even without humans on board - it could easily double as a cargo ship.
You could accelerate it gently, at a hundredth of a g - if we had an easy way to do that - and so go anywhere in the solar system given enough time. Or make it into a Mars cycler continually traveling between Earth and Mars - or a Venus cycler doing the same for Venus. Neither of those require rapid acceleration.
But it wouldn't be able to land on any of the planets, or larger asteroids.
Anyway, I think, not too likely that this will happen before it has to de-orbit. But depends, progress can be rapid sometimes. It could be used as an interesting story-line in a near future science fiction story.