Ran out of fuel it too shallow answer.
There should be something else like uncontrolled spinning and making waste radio noise. But this could be good experiment how long probe would survive so close to sun.
When Mariner 10 ran out of fuel, it no longer had the ability to point its high-gain antenna at Earth. There was no benefit to leaving the radio on, and leaving it on meant there was a chance its transmissions would interfere with other missions, so it was switched off.