Troubleshooting a PWM-field effect transistor driver board
No, judging from the solder flow on the pads of C6, there was never a part placed there. If there once was a part placed there, then you would see broken ends of the component still in the solder, or a badly mangled solder ball/pad.

Intentionally unpopulated components are common in manufacturing. Multiple products may be manufactured using the same board, or the pads for a component were included in the design so a component could be soldered in place for evaluating circuit performance. 

Beyond that, without a circuit diagram there really isn't anything we can tell about what the circuit was intended to do let alone what went wrong.