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*
Modern authors(early twentieth century literary movement) did this to force readers to look for and feel the pace and flow of the book created by the author's language by removing the crutch of chapter breaks. A well-written novel that is not plot-driven is not well-served by chapter breaks. They unnaturally break up the reading experience. However for genre novels and plot driven novels they are necessary and helpful.
The first volumes of Proust are written without chapters and are the best writing that there is. Hermann Broch wrote novels with only three sections instead of standard chapters that are amazing.
I stop when I find I have to keep going back and rereading a section because I'm asleep with my eyes open. I seldom do that though. My problem is I stay up to all hours reading a good book when I should be sleeping.