Some people do. If you train in the morning in a fasted state you could eat afterwards between e.g. 09:00 and 17:00. I have tried it but I am hopeless lifting weights in the morning.Can you do this while lifting or is it diet only?
There are people on the running thread who run in a fasted state, I usually prefer to eat something up to 90 minutes before a run and I wouldn’t run over 6 miles in a fasted state.