It really depends on what kind of slavery and when you're talking about.

Plato's Euthyrphro starts with the interlocutor taking his father to court for the death of a slave (a charge that he seemingly never went through with). Whether Euthyphro could ever have successfully gotten his father in trouble is debatable since Athenian law only allowed family members to prosecute someone for murder. A slave has no legal family and therefore no one (perhaps) could legally step in to defend them. On the other hand, if you lent someone a slave and they then beat or killed said slave, you could take them to court for damaging your property.