Per the film's official novelisation, Nero's ship, The Narada was destroyed utterly, torn apart into fundamental particles, then fed directly into the maw of a black hole and crushed into the singularity at the centre.
The main bridge screen offered a final glimpse of the Romulan commander they had known as Nero: defiant, half-mad, and ultimately frustrated as he joined his ship in being crushed down into his subatomic components.
Star Trek - Novelisation
Note that Nero was unable to use the singularity to enter a different timeline
In the absence of full warp power there is no possible way you can attempt to escape by utilizing the anomaly to attempt a time shift — you have no maneuverability. None of you will survive without assistance — which we are willing to provide.”