I’ve found some useful information on the Edison Hardware Guide https://communities.intel.com/docs/DOC-23158
It states that the FAULT pin is a USB power fault input (from external USB). It also states that Two signals PSW (pin 21), and FAULT (pin 19) from the ULPI controller are used to control the external power switch and monitor the overcurrent condition on VBUS. The PSW signal is active high and controls an external VBUS power switch or charge pump. The FAULT signal is active low. FAULT should be connected to GND if USB host mode is not used.
According to this and what you are saying I believe you should connect it to ground. Take a look at the last line of the previous message “FAULT should be connected to GND if USB host mode is not used.”. You are not planning to use USB host mode right? If you don’t plan to use it I’d follow the instructions of the guide. In the guide you will find information of other ways to power the board.