PA28 pilot reported while landing at a non-towered airport with an electrical failure they observed an aircraft depart opposite direction and fly over them.

Narrative

On Day 0; at XA:32 local time; while experiencing an in-flight electrical system failure; I was the pilot in command of a PA-28R-200 that landed on Runway XX at ZZZ while a P28A was departing Runway XY at ZZZ. I didn't see the other aircraft during my final approach as it must have back taxied on Runway XY. I observed the other aircraft's landing light coming toward me as I flared for my emergency landing; and veered to my right (toward the south half of the runway) to avoid the aircraft. The other aircraft rotated without incident and passed overhead by approximately 100-150 feet. I was operating a PA-28R-200 I rented for personal use from an FBO on a VFR flight from ZZZ1 to ZZZ at 8;500 ft. MSL. A private pilot-rated passenger was riding along.The Electrical Failure. At approximately XA:20 local; and roughly 10 miles East of ZZZ; my aircraft began losing electrical systems; starting with the radio. By that time; I had already reported my aircraft's position and intent to land at ZZZ; but I am unsure if those transmissions went out; as the electrical system was beginning to fail. As the radios failed first; my private pilot-rated passenger and I began troubleshooting avionics circuit breakers while descending into the ZZZ area. The Garmin 430 and digital engine-monitor failed simultaneously; and the only remaining electrical equipment was the transponder. I squawked 7600; and used the radio's emergency function to broadcast my landing intention on XXX.X. Another pilot reported that I was broadcasting 'on guard'; which I confirmed and reported the electrical failure and intent to land at ZZZ on Runway XX. At this point I was approximately 5 miles East of ZZZ. Moments shortly after my communication on XXX.X all electrical systems were lost; including the transponder. The discussion on XXX.X was the final radio transmission the aircraft received until the aircraft was on the ground. I continued to key the mic and attempt to call position reports in the pattern; but it seems they did not broadcast given the electrical failure. Choosing Runway XX. Prior to loss of radios; I'd been monitoring the CTAF for ZZZ for at least 30 miles of flight. Around XA:15 local; I heard an aircraft making position reports for landing on Runway XX at ZZZ. The ASOS report I received approximately 5 minutes earlier reported winds variable at 4 knots. Through ADBS linked to ForeFlight on my battery-operated iPad; I was able to observe that aircraft; a Decathlon; approach and land on Runway XX at approximately XA:18 local. That Decathlon was the only other ZZZ radio traffic observed during the event. As the electrical failure transpired; and realizing that I couldn't transmit or receive; I opted to enter the left downwind for Runway XX as I knew that runway has been recently used and the winds were variable. Entering the downwind; while my passenger and I continued to cycle the alternator and troubleshoot the electrical failure; I did not observe wind sock readings or other information that would lead me to believe another runway was optimal for an emergency landing. As I was mid-field downwind; I saw the P28A holding short of Runway XX/XY on Taxiway 1. I'm unclear if that pilot observed me in the pattern directly ahead of his plane. Reviewing the track log from my coupled ForeFlight and SentryPlus; I was around 500 feet above the standard traffic pattern altitude at midfield downwind. Landing. As there were no functional electrical systems in my aircraft; I was unable to confirm whether the landing gear was down and locked safely for landing after operating the landing gear toggle. Consequently; I opted to utilize the emergency gear release lever to ensure the gear had deployed and would likely be locked for landing. In order to perform this task I extended downwind approximately 2 miles; and then turned base and 2 mile final to Runway XX at approximately XA:30 local. The PA-28R-200 I was flying had a known inoperative landing light before the flight; and with the electrical failure; I didn't have much practical way to make myself more visible while trying to land as soon as possible. I did not see the other aircraft on the runway; which was likely back taxiing on Runway XY at this point. I saw the other aircraft's landing and taxi lights as I was flaring to land on Runway XX approximately 10ft AGL. Given the ongoing emergency situation in our aircraft; and the long runway; I did not to perform a go-around and instead focused on getting my aircraft to my right and out of the path of the other aircraft in the event it aborted its takeoff and stayed on the runway. My landing gear were down and my landing was uneventful. The other aircraft rotated long before reaching my aircraft on the runway. It overflew my aircraft by approximately 100-150 feet and turned to the south earlier than would be standard for a traffic pattern. My aircraft was able to exit the Runway on Taxiway 2 and taxi to an FBO via Taxiway 3. I learned later that the pilot of the P28A did see us at some point in his takeoff process; but hadn't heard any reports by us. Follow Up. The PA-28R-200 I was flying remains in maintenance at ZZZ as of the date of this report. Maintenance identified a frayed and fouled battery connector cable and loose battery terminal connector that likely led to loss of battery power in flight. The alternator appears to function appropriately. I've reviewed the situation with my flight instructor; who flew to ZZZ to pick us up the day of the event. I plan to carry a hand-held Communication Transceiver in my flight bag going forward to ensure backup communication capabilities. Please do not hesitate to contact me for additional information including other aircraft tail numbers; tracking data; etc.