Would Slavery Exist in the Ideal Minarchical Society?

Minarchism is a form of Libertarianism, with the philosophy that the ideal government would exist to provide only a few necessary services to the people. It often limits the State to three institutions, that could not be handled properly by the free market, the military, the police, and the courts. The actions that these three institutions would provide would be to protect citizens from aggression, and protect their property laws and natural rights. Now, I go back and forth between whether or not slavery would exist in this ideal Minarchical society, as the government would ideally protect citizens' natural rights to life, liberty and, property, and therefore, society would not allow slavery. Yet, this line of thinking becomes problematic, because who/what would decide who is a citizen and who is not? I go back and forth in my mind and was wondering what you guys think? Ultimately, I believe slavery would exist as there is no definite way to define who or what would be a citizen in this society, yet my mind is open and my opinion is subject to change on this topic.