[Pearls Before Swine]

Who broke an oath?

Jon Snow... he's abandoning the Night's Watch.

But, whether that makes him an oathbreaker or not is open to discussion. He swore to stay with the Watch until death, but he died. The question is, "does he have to re-up?"

[Tanniker Smith]

When they die (even if they didn't show this) the words spoken over the body are "His watch has ended."

You have to assume that over that day he was dead, someone mentioned it.