Learning isn't shift-based. If one is caring for a sick patient, finish it. Don't clock out. I'm an Anesthesiologist and even I still check on my patients for days related to the outcomes of their surgeries. And that's because I take my PROFESSION (not a job) seriously, and I do care about the health of the people I treat.

I was a fellow once too, and the hours do seem ridiculous. But, when you are an attending, you may be in a practice where it's just you. You are it. Always on the clock. This is training for being an attending.