I try to read until I reach the end of the chapter, but have stopped before that if I dozed off. I used to be a stickler for going to the end no matter how tired I was... until everything was gibberish. lol.
No matter how much I tried plowing through w/ my eyes barely open ~ slits is an understatement ~ it just wasn't jelling, so I put the book aside to sleep. How could I enjoy a book if it makes no sense to me when I'm tired. Not fair to me or the author who get their all to be appreciated.
Still, I do try to make it to the end... *g*
I stop reading when I'm tired too. True, true...it's no use trying to read more when the eyelids just keep getting heavier and heavier! :D But if it's a bad book, I'll stop at the end of the chapter and move on to something else.
If I am reading during the day then I will stop wherever, use a bookmark. However if reading at night then I usually stop at the end of a chapter. Quirky but it's what I do.