Sorry when you take the props off, the electrical current drops.
Loose prop nut will not cause burned motor. You can run these brushless motors without props and they are just fine. You can always "underprop" but you get overheating and problems if you "overprop".
Generally what happens is that a crash disconnects or breaks a wire. The motor can't run with only 2 of 3 wires attached. On next flight, if you give lots of power to try to start it, it will burn up. If you only give a small amount of throttle and notice that a motor is not starting, you probably won't burn it up.
So at this point, you need to make sure the ESC is not damaged, or you may burn another motor when you hook it up. I suggest a current limited power supply when you first run it again, or replace both the motor and ESC. Simply inserting any large automotive light bulb in series with the battery will limit the current.