What conditions existed that would allow for slaves to be property owners

As slaves, I don't think they could own property of any kind.

http://www.ushistory.org/us/6f.asp
(2nd paragraph)

The only situation I've ever read about was if/when slaves managed to get enough money together (and that would have taken a great deal of secrecy), they could buy their freedom if their masters were willing to sell.
http://www.google.com/search?q=could+slaves+buy+their+freedom&oq=could+slaves+buy&aqs=chrome.0.0j69i57j0l4.4342j0j7&sourceid=chrome&ie=UTF-8

The conditions that allowed slaves to be property owners were relatively rare and specific. Slavery, in itself, involved the ownership of individuals who were treated as property, without legal rights or privileges. However, there were a few exceptional circumstances where slaves were permitted some degree of property ownership. Here are a few conditions that contributed to this:

1. Customary practices: In certain cultures or regions, customary laws and practices allowed for limited property ownership by slaves. These practices might have developed over time due to specific economic, social, or cultural factors.

2. Informal arrangements: Some slaveholders, particularly those who owned domestic servants or skilled workers, might allow their slaves to possess some personal belongings or even acquire property informally. This was often based on a master-slave relationship built on trust and mutual interests.

3. Manumission: Manumission refers to the act of freeing a slave. In some cases, slaveowners might grant freedom to their slaves as a reward for exceptional loyalty, service, or some other reason. Upon being freed, these former slaves could legally own property like any other free individual.

4. Legal loopholes: In rare instances, slaves were able to legally acquire property due to certain loopholes in the legal system or unique circumstances. For example, if a slaveholder died intestate (without a will), the laws of inheritance might allow slaves to inherit property, albeit with restrictions.

It's important to note that these conditions were the exception rather than the norm. Slaves generally had limited legal rights and were considered as property themselves, rather than owners.