Oh, I see a typo in the previous post. Too bad this forum doesn't have an edit feature. Pity.
Exodus Chapter 21:20
(20) If a man shall strike his slave or his maidservant with the rod and he shall die under his hand, he shall surely be avenged. (21) But if he will survive for a day or two, he shall not be avenged, for he is his property.
"the rod"
In some English translations, the definite article "the" is ignored. However, this verse does not refer to just ANY type of rod (which would be the meaning if "the" is omitted). Rather, this verse is referring to THE specific type of rod that was designed for slave owners to enforce discipline. "The rod" refers to that specific type of rod that was customary for a slaveowner to carry.
This rod was just like the sort of thing that a modern day parent might use to discipline his or her own children, it is not the sort of rod that would cause injury when used properly. Only if the slaveowner (or parent) used the rod viciously and excessively, would the slave (or child) be killed.
Therefore, if the slave died within 24 hours after the slaveowner used the rod, this was convincing evidence that the slaveowner (1) used vicious force (2) for a lengthy duration of time and (3) must have seen that he was killing the slave. This combination of factors would be strong evidence of deliberate murder. If convicted of murder by a Jewish court of law, the slave owner would be executed; that is the punishment for murder.
"a day or two"
In a time and place without modern emergency rooms and life-saving technology, a murder victim would typically die within 24 hours after being attacked. If the slave lived more than 24 hours (which is the legal meaning of the phrase, "a day or two"), then the slave owner's intention to murder becomes doubtful, making this a case of manslaughter at worst. And perhaps the slave met his demise another way entirely, making the slave owner innocent of the slave's death entirely.
"his property"
First, it's assumed that a person would not intentionally destroy his own valuable property. If your mercedes benz gets trashed, nobody would suspect you did it yourself - unless there was strong evidence overwhelming this natural assumption of innocence (such as the slave dying immediately after the owner uses the rod).
Second, once doubt is cast on the owner's intention to kill the slave, the case becomes one of manslaughter at worst. In this case, the death penalty does not apply. Instead, the punishment could be one of monetary compensation. However, since the slave was his own property, the owner would be essentially compensating himself. Monetary compensation to himself, for accidentally destroying his own property, doesn't make sense. Therefore, there's no punishment.