Where in Rome were the hopelessly sick slaves taken to die?

In Rome, every well-to-do master had slaves. Landowners in different parts of the country had dozens of slaves. They worked on the land, the chief slave supervised their work. It was very profitable to maintain such a workforce, once a year they were given clothes, and one shoe even less often. There was no respect for the sick and dying slaves, they were not treated or even buried. As soon as a slave became useless due to old age or illness, he was taken to an island on the Tiber River, where he died without food and care.