Ok mate, the current draw (amps) of motors is basically a product of a number of things, the kv of the motor, which governs the speed the motor tries to spin (for a given voltage and throttle value) and the propeller which basically fights the motor, putting load on it. If the prop is too much for the motor it is called "over propping", the motor with draw massive amounts of current without the corresponding increase in speed of rotation (it just lacks the torque)
The current is therefore "pulled" from the motor.
If the amp draw gets too high the motor will melt (or the windings will)
However before that point the amp draw may exceed the capability of the esc, causing that to literally burst into flame.
That all assumes the lipo is capable of delivering the amps.
If you try and pull too much out of a lipo it will puff up and eventually go up in a ball of smoke and hissing.
Overpropping of any sort isn't a brilliant idea, the motor becomes inefficient, heat degrades the magnets, heat in the lipo shortens its life etc
You avoid it by working out your currents properly.
To give you a current (see what I did there ? :)) example:
I am about to upgrade one of my dquad obsessions, I have tmotor f60 pro 2500kv arriving tomorrow and wraith32 escs arriving next week so I thought it may be interesting to try and push the motors or esc beyond their limit.
I am running returner r4 2206 2300kv motors, spedix es25 escs and racekraft 5051s, I set the cam angle to about 70 degrees and kicked the crap out the throttle,
I can not get the motors to do anything more ham get slightly warm, the escs remain cool, but the lipos are quite hot and I am using tattu r-line 1300mah 4s 95c lipos, they are good lipos, if I continue like this all I am gonna achieve is puffing up one of my batteries. They should be able to provide 123.5amps constant and double that burst, no way I am drawing over 100 amps constant but if I continue they are not long for the world, (all battery specs are naff)
So gonna have to find another way to dispose of escs and motors.