I can't speak for the Roman Republic (Edit: Looks like /u/XenophonTheAthenian has that covered), but in the United States, slaves could not legally own property in most places. Therefore, a slave owner in the United States could definitely confiscate their slaves' goods. However, this was rarely done for a variety of reasons. First your slaves would be very upset and you might provoke some serious problems or even violence. Consider that on a large scale plantation a slave can run away fairly easily. If he or she does so during harvest time (when the planter needs every person available to get the crop in) this can have a very large negative impact on the profitability of the plantation. Of course, such a runaway would probably be caught and punished, but the damage would already be done. There's quite a lot of evidence to suggest that slaves knew their value during harvest time and acted accordingly. So, slave owners couldn't act with total impunity to their slaves. In fact, some plantation owners paid their slaves a wage during harvest time under the table to get them to work harder.

Some slaves earned some extra money on the side, either through their own labor or through theft. Whatever they were peddling could be sold to other slaves or even poor whites in the area. This could help the slave in question, but was also dangerous. If a poor white ripped off a slave there was little that slave could do to gain recompense.

You also have to consider the fact that in most places in the United States slaves simply could not purchase their freedom. It was actually illegal in many states. The caveat here is New Orleans for much of the antebellum period, which not so coincidentally, was a French and Spanish colony rather than a British one. There I have found through some of my own research that slaves employed by the city were occasionally paid an official wage.

In the Caribbean the situation is somewhat different. The French, Spanish, and Portuguese all had much higher rates of slave manumission and allowed slave to purchase their freedom even after the Americans made it illegal. Plantation slaves had little chance to purchase themselves due to isolation, but urban slaves occasionally entered into deals with their masters where they would pay a lump sum and continue to pay part of their wages to their master for a certain amount of time. Occasionally the master would simply steal the wages or the sum and continue on with their day, so to speak. In this case the slave would have to take his master to court. A long and difficult process with no secure outcome, since it was frequently difficult to prove such a deal had existed in the first place. However, there are examples of slaves successfully taking their master to court in Latin America.

So, long story short, yes it was possible that an owner could confiscate their slaves' wealth and it certainly happened, but there were also many reasons for a master to think twice before doing so. Though there was not a legal recourse for a slave in the United States, there were still ways to get back at the master. In Latin America the situation was a bit different, but still a lengthy and difficult proposition.

Further Reading- Jeff Forret, Race Relations at the Margin, Cowling, Conceiving Freedom, Follett, The Sugar Masters, Baptist, The Half Has Never Been Told (Note: There are some issues with this book that are still being discussed in academia right now), Reis, A Slave Rebellion in Brazil, Block, Ordinary Lives in the Early Caribbean, Hall, Social Control in Slave Plantation Societies. (There's a lot more, but these are the ones that immediately spring to mind.)

Laws on slavery and servitude vary wildly across locations and periods, and none of these societies conceived of slavery the same way. By Roman law slaves had no legal right to direct ownership of property of any kind. So strictly speaking a slave had no wealth to confiscate. In practice this was not strictly true. Slaves (and children who had not been manumitted as well, since they also had no legal right to property) could be and often were granted a sort of allowance called a peculium. The peculium is often called an "allowance," but it's not really. Rather than something that was given to a slave or child and constantly provided by the master or father, the peculium was more like an administration of assets legally owned by the master or father. Peculia could be quite large, including not only money but also land or even other slaves. For example, one of Trimalchio's slaves in the Satyricon gifts a slave that he owns as part of his peculium to the main characters. Which brings up another aspect of the peculium: since the peculium was a legal administration of the master or father's assets that was independently used by another, the slave or son holding a peculium could enter into transactions with it. This might be sale of elements of the peculium (land, slaves, etc. Some peculia actually included the administration of businesses or farms or could be used to purchase shops and stuff) or purchase. Generally the statuliber, the slave who purchased his freedom, would pay his purchase price using his peculium, which he had increased (since presumably he would not usually be given a peculium equal to the price of his purchase). Statuliber is a funny concept, however. Technically a statuliber is a slave legally manumitted after the fulfillment of a certain condition. This condition was often simply the passage of a certain amount of time or was considered fulfilled upon the execution of the master's will and testament in which the slave would be written as freed. But slaves who purchased their freedom were considered statuliber for having provided a certain amount of money to the master. Technically speaking this is not purchase, because those assets were legally the master's--legally the slave was not increasing his own property (though this is how just about everybody conceived of the peculium in practical terms) and entering into a transaction with his master to purchase his freedom, but was instead increasing the value of his master's assets on the condition that he would be freed after providing a certain amount for his master. Legally, then, at least in theory, the master could decide to revoke the right of peculium, thereby removing the slave from legal administration (de facto ownership) of that property. But this cannot have happened often, if it did happen at all--a master who would make the decision grant his slave a peculium cannot frequently have been the sort of person to perversely remove that right

I am late to the party, but there is a slave narrative written by a man who had to buy his own freedom three times because his owner kept the money and sold him instead. The third time only worked because he arranged for a white man to use his own money to buy him. He was a canal navigator named Moses Grandy and you can find his narrative for free here: http://docsouth.unc.edu/fpn/grandy/menu.html

You can actually find scores of free slave narratives on the website above. Here is a wikipedia article: https://en.wikipedia.org/wiki/Moses_Grandy