PA-34 flight instructor reported the left engine failed shortly after liftoff. Flight landed safely on the remaining runway.

Narrative

I was the CFI/PIC (pilot in command) of a Piper PA-34-200 Seneca I; conducting an instructional flight at ZZZ. This was my third training flight of the day. On the flight; we completed two touch-and-go landings and one full-stop landing at ZZZ1. On the XA:00 flight; we completed one touch-and-go at ZZZ and one full-stop at ZZZ1. The XA:00 flight was the first touch-and-go of that lesson at ZZZ Runway XX.At approximately 105 mph and 150 feet AGL after liftoff; I heard a loud bang followed by strong vibration. I immediately took control of the aircraft; verified all engine controls were full forward; and observed the left engine feathering on its own. With runway remaining; gear down; and adequate airspeed; I elected to land straight ahead.The touchdown was normal on Runway XX. Breaking was applied firmly; but the aircraft was unable to stop on the paved surface and came to a complete stop a few feet into the grass beyond the runway. The aircraft was secured in accordance with the checklist. There were no injuries.A post-flight inspection revealed heavy oil contamination on the left engine cowling; wing; landing gear; and left elevator. After authorization to open the cowling; a full-length crack was observed in the left engine crankcase; extending from top to bottom. The main right tire was also found flat; likely due to heavy braking. No other structural damage was noted.