EMB-190 Captain reported a LH/RH BRAKE FAIL and FAULT messages on approach and elected to go-around to troubleshoot. The flight crew then performed a precautionary landing and with no brakes available; used reverse thrust to slow the aircraft to a stop.

Narrative

Passing 9;000 ft. on descent into ZZZZ; we received a LH/RH brake fault; followed by LH/RH brake fail. We climbed back to 10;000 ft. to run the QRH. The QRH advised us that no brakes will be available. Unsure if landing in ZZZZ would be an option with Company; we held as close to ZZZ Center as possible. We ACARSed Dispatch and went through our options. Name; our Dispatcher; talked to Maintenance and advised to continue to our destination. The runway was 11;000 ft.; running the landing numbers; we came up just shy of [the] 8;000 ft. needed to land safety.I advised the inflight crew members of the situation; and told them we were in a code yellow. Made a PA to the customers; informing them that there was a possibility of partial brake loss; but that the runway in ZZZZ was more than adequate to land safety. [We requested priority handling and] proceeded on the approach for Runway XX. Upon landing; no brakes were available. I used full reverse to a stop - a normal landing except for the additional runway length. I set the parking brake; and asked inflight to remain seated; remain seated." I called them to make sure they and the customers were ok; everyone was fine. I then made a PA and informed the customers that since we had no brakes; a tow to the gate was necessary. Once at the gate; passengers deplaned and Maintenance started working on the issue."