One wire (usually with a loop, aka breakaway cable) connects somewhere to the tow vehicle. If that is the one broken, you will have no emergency activation if your trailer somehow loses it's connection with the hitch. If it is the power side of the switch, power will not be applied to the brakes of the breakaway switch is activated.
I have damaged the break away cable before. You can take that cable along with the connecting pin to a RV supplier or store and get a match. Note that if you pull the breakaway cable with it's connector out of the switch, please be sure to pull a battery cable off otherwise your trailer brakes will be locked on. Leaving that pin out will drain your battery or could overheat the brake magnets dependent on the charge of the battery and how long the pin is left out.
'04 Classic 30' S.O.,'03 GMC Savana 2500,'14 Honda CTX 700