Air carrier First Officer reported that windshield wiring short circuited; caught fire; and cracked. Flight continued and landed without issue.

Narrative

At around 1000 feet AGL; after fully configuring the aircraft for landing on the ILS XX approach into ZZZ; we noticed a bright light coming from the bottom of the right side windshield. Initially we thought it had to be a lazer pointed from the ground; but quickly realized that part of the windshield heater wiring had short-circuited and caught on fire. The wiring burned for approximately 5 seconds and then stopped. Less than 10 seconds later; before any action could be taken; a loud bang occurred and the entire FO side windshield cracked. Still up to this point; no EICAS messages were displayed. Since we were fully configured and about 500 feet above the runway; we quickly decided that the most prudent thing to do would be continue and land the plane. We did not notify ATC at this time because the tower in ZZZ was closed and we were communicating on the advisory frequency. We landed without issue; and once we cleared the runway we got an EICAS warning for WINDSHIELD 2 HTR FAIL. We then proceeded to the gate and contacted maintenance immediately.