live off something—
1. use smth. as food:
- Some animals live off plants, whilst others live off other animals.
2. get enough food or income from smth.:
- He had lived off his vegetable patch on the farm and off the sales of some cattle.
live on something—
1. eat certain food as one’s regular diet:
- They live on fish, coconuts, and tropical fruit—papaya, bananas and mangoes.
2. = live off something 2:
- Maugham knew that he had to court popular taste if he wanted to live on his writing.