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Hi Jack,
For your setup the common-mode voltage is set by the input to non-inverting input of the op-amp. From the data sheet section 6.3, as you can see the input common mode voltage range (Vcm) is between 0V to Vcc - 2V which translates to 0V to 10V for your case. With a Vin of 14V you're clearly violating this condition. Operating outside Vcm range will lead to unpredictable op-amp behavior. I hope this help!
When VIN is 14V, the input current will drop from -20nA (normal input bias current) to 0 nA.
Both inputs should be greater than upper common mode, so output could go low or high as the input stage is cut off.
If output wants to go high then output will be close to 10.7V, the VOH level of this device (room temperature).
If output wants to go low then output will fall until inverting input is back in valid range which is close to 10.7V.
Notice that both invalid range possibilities produced the same output voltage.
No it won't short, the LM2904 doesn't mind 14V on the input(s).
