ROME — The coronavirus was already a disaster for Meorina Mazza. In March, it sickened her brother, killed her cousin and prompted officials in Italy’s southern region of Calabria to quarantine her seaside town of San Lucido.

But the lockdown also cut her off from her off-the-books shifts as a kitchen hand and made it harder to apply for welfare. Now she is relying on donations of flour to feed her daughters, but still has no money to pay her electricity bills.

“We are really headed toward total desperation,” said Ms. Mazza, a 53-year-old mother of two.

Italy’s coronavirus epidemic, among the deadliest in the world with more than 24,000 deaths, first exploded in the country’s wealthy north, where it stretched one of Europe’s most sophisticated health care systems to the limits. But it is the country’s poorer, less developed south that has loomed over the entire crisis and figured prominently in the government’s decision to lock down all of Italy last month.

Now, with the Italian government’s plan to begin a gradual reopening of the country on May 4, some southern leaders remain so fearful of the potential of the virus to devastate their regions that they have suggested they would ban northerners if they rushed to lift the lockdown.