The death penalty appears to be a Heavenly one. The obvious source in Tanach is Jeremiah chapter 28, where a false prophet called Hananiah prophecies that Nebuchadnezzar's rule would be overthrown within 2 years and Judah restored to its own sovereignity.
Jeremiah responds firstly with "so it may be so.." but warns Hananiah about false prophecies and then passes the word of G-d that he will die within a year, which he does.
Sanhedrin runs through laws regarding prophets and prophecies. In general, a "bad" prophecy might be overturned (e.g. Jonah) through "teshuva, tefila and tzedaka" but a good one will always come to pass (unless it's a false one).
With regards to the "detail". it's often in the detail that it becomes clear that the prophecy was a true one. We see this a lot with Elisha. For example, the price of flour after the famine, and what happened to the king's steward who laughed at the prophecy. (The first is an example of a good prophecy. If that hadn't happened it would have meant Elisha was a false prophet. But of course he wasn't. With regards to the second, if the steward had responded "I have sinned before Hashem" and done a true teshuva, that one might have been overturned).