The adjective liber in Latin is what the slaves are not, that is, "unrestricted [people]". The root 'lewdh-, from which it comes, is also in Leute and ljudi (people). Liberty today seems to be often used to mean unrestrictedness of capital/property/contracts, so the connection I see with its semantic history is the idea that some people can be more people than others, and that the government should be strong enough to deter anyone from threatening this state of liberty (e.g. back then by fleeing from slavery, now by ... well the list is too long). Remember the words of Laozi, long and short give rise to each other.