How to fix this wifi FPV antenna
Frequency is not given, but this looks like it could be based on a quarter-wavelength antenna main element (your broken wire), and a quarter-wave sleeve balun element:

 Coax cable extends into the left end of the metal sleeve, which is hollow. The left end of the sleeve is electrically floating, unattached to anything. The right end of the sleeve is attached to the coax shield.
Coax centre conductor is attached to the quarter-wave antenna wire, where it appears at the right end of the sleeve.