All the ideas I have for a post solar apocalypse have already been mentioned and described well. Food chain issues would be our main priority and lets not forget, the worlds supply of fresh water would go as no rain would deliver it to the land.
Now, might we also consider that if the Sun was removed from the solar system, the earth would fly off at about 30,000 mph and could impact the asteroid belt, at it's present orbit, in just 77.77r days. I doubt we'd survive that.
However, the orbit of the asteroid belt itself would disturbed to and affected more by Jupiter's influence, relative to their positions in space, which might fling asteroids towards us before we get to the congested area.
But assuming that enough asteroids are left in the path of Earth as it exits what was our solar system, in about 80 days we'd be like a target in a cosmic firing range.
IHI