Or even know precisely where the scene of battle occurred.

Knowing the system alone is not enough. Given the base velocity of the debris cloud(s), even a few hours would be sufficient time to allow enough separation to make finding all but the largest hulls difficult. And that assumes one is free to use active sensors. If the battle happened in an enemy held system, nobody is going to be broadcasting an emergency locator signal unless their situtaion is absolutely desperate (e.g. capture being preferable to death).