Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (mon) 11
Situational Awareness
ATC Issue All Types; Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Landing Without Clearance
Air Traffic Control Provided Assistance; Flight Crew Landed in Emergency Condition; Flight Crew Overcame Equipment Problem; Flight Crew Executed Go Around / Missed Approach
Aircraft
Aircraft X; a local pilot was returning from a 15 minute local flight. I cleared them to land and the instructor said 'going around' abeam the numbers. I instructed them to make left closed traffic. Aircraft X was executing the left crosswind turn when I heard them say something garbled. I asked them to say again and I heard 'lost our engine coming back'. I cannot recall if I recleared them to land; but did ask if they needed assistance. I then reached for the crash phone. Aircraft X was able to land on the remaining length of runway and stopped just short of the end of the runway. Airport Rescue and Fire Fighting (ARFF) units and Operations were dispatched and I maintained radio communications with the pilot; who stated they were not hurt. I notified TRACON; the airport; and later my Air Traffic Manager. At the time I was alone in the Tower working all positions combined. Traffic was light; but I recalled another controller back from break to assist me while I finished the proper paperwork.It is not unusual to be working alone at this time since there are only 2 controllers left and we need breaks. I have a personal connection to this particular pilot and wanted to be sure they were okay; which is why I reached for the crash phone first; and cannot be sure I re-cleared them to land. Additionally; I would like to suggest a more streamlined; facility specific checklist for incidents.  The paper checklist is very convoluted with lots of form numbers etc. My main priority was to get the ARFF dispatched; notify the Operations and worry about the pilot and aircraft; then get to the checklist and paperwork.
PSP Tower Controller reported an aircraft in a traffic pattern that lost their engine and potentially landed without a clearance.