Ancient Rome covers quite a long time period and Roman tax collection changed quite a bit in that time. I will focus on the late Republic (think Caesar). Although I can assure you that slavery had nothing to do with back taxes.

In the late Republic Roman citizens did not have to pay annual taxes. It had been that way permanently since the end of the Third Punic War when Rome had enough control over foreign lands to extract enough money to pay for public works. Rome calculated taxes for provinces at a base line of one twentieth of their produce. In reality the Senate heard bids from private contractors called publicani for who could get the most money out of a province. These people hired tax collectors to go around from town to town to get as much money as they could from the locals, hence their bad reputation in the New Testament.

These contracts were very competitive and the men who held them had a lot of away in Rome and were behind a lot of political decisions focusing on expansion and changes regarding the administration of the provinces. Cicero was a vocal supporter for example. Roman magistrates overseeing the provinces provided protection and force for the publicani if need be as well as public services supported by the taxes.

I can provide some further reading later (I'm mobile at the moment) if you are interested.

In the late empire, the Decurion class was expected to pay the taxes for the region they administered. So, just imagine if your local city counsellor was tasked with collecting your municipal taxes and if you came up short, they had to make up the difference themselves. This led to extortion and exploitation by those Decurions not wanting to, or unable to, pay out of pocket and/or people abdicating their position as Decurions.

Source: Treadgold, Warren A History of Byzantine State and Society 1997 Stanford University Press.