If you refer to the fag end of something, you mean the last part of it, especially when you consider this part boring or unimportant. He never had much confidence in his judgement at the fag-end of the working day. the end of a cigarette that someone has finished smoking (fag (15-18 centuries))
the frayed end of a length of cloth or rope the time of the last part of something; "the fag end of this crisis-ridden century"; "the tail of the storm
A condition to which male high school and college students are prone consisting of difficulty in concentrating, mild forgetfulness, and difficulty in maintaining a train of thought, arising from "too much thinking". Physical symptoms can manifest as well
drained of energy or effectiveness; extremely tired; completely exhausted; "the day's shopping left her exhausted"; "he went to bed dog-tired"; "was fagged and sweaty"; "the trembling of his played out limbs"; "felt completely washed-out"; "only worn-out horses and cattle"; "you look worn out"