Sometimes I'll offer a draw if I'm losing in an endgame where my opponent has a slight piece advantage hoping they'll accept out of not knowing the proper techniques or not wanting to put forth the effort.
I've had funny draw offer situations too. One where an opponent declined a draw and then instantly the next move drew the game by going along with threefold repetition. Another where a draw was declined and they blundered and I came back to win.
Why is it that people offer draws as a last ditch effort in a clearly losing position? Just about every game I've won so far has someone offering a draw, and most of the games I've drawn have been because I accepted in a winning position. I always accept if it won't hurt my rating just because I try to be nice. But still, I think it's poor sportsmanship and I am amazed how many people do it. Kind of puts you on the spot and makes you feel compelled to accept.