You're allowed to go buy groceries or medicines in case you're living alone. And you're allowed to work.How does this actually work? Are you allowed to shop or to work out? And if so, isn't it quite a soft sort of punishment?
Normally you're not allowed to go outside for any other reason, unless you get an exemption.
Most Italian jails are overcrowded. That's why house arrests are prevalent for "minor" crimes.