I noticed a weird sound coming from under my mazda 3 when I was parking it to my garage. I checked under my car to check what was causing the noise and saw this broken black cable. What could this cable be? Is it safe to drive with this thing hanging underneath my car? It's driving me nuts. I can't go to the service center as it is closed atm.

 

Two things. Does the emergency brake work? Are you sure it is attached to your car? You may have ran over it and it flipped up under your car.
One other thing, you front inner CV boot is starting to leak or looks awfully shiny. Maybe whatever it is was rubbing on the boot making it look shiny. and it finally fell down.