A separate body of common law developed from trials, held sometimes in the Forum, sometimes in the Senate.
When the law was short and simple, the saying "Ignorantia juris non excusat" (ignorance of the law is no excuse) made sense. But as the government and its legislation became more ponderous, the saying became increasingly ridiculous. Eventually, under Diocletian, law became completely arbitrary, with everything done by the emperor's decrees—we call them Executive Orders today.
I've mentioned Diocletian several times already. It's true that his draconian measures held the Empire together, but it was a matter of destroying Rome in order to save it. As in the U.S., in Rome statute and common law gradually devolved into a maze of bureaucratic rules.
The trend accelerated under Constantine, the first Christian emperor, because Christianity is a top-down religion, reflecting a hierarchy where rulers were seen as licensed by God. The old Roman religion never tried to capture men's minds this way. Before Christianity, violating the emperor's laws wasn't seen as also violating God's laws.
The devolution is similar in the U.S. You'll recall that only three crimes are mentioned in the U.S. Constitution—treason, counterfeiting, and piracy. Now you can read Harvey Silverglate's book, Three Felonies a Day, which argues that the average modern-day American, mostly unwittingly, is running his own personal crime wave—because federal law has criminalized over 5,000 different acts.