Cessna 402 Captain reported engine roughness during cruise. Flight returned to departure airport and landed safely.

Narrative

Aircraft was in cruise at 2;000' direct to ZZZZZ from the northeast with the student as PF when we experienced initial left engine roughness. An adjustment to enrich the mixture appeared to solve the problem; but it reoccurred after entering the course reversal for the upcoming approach. The instructor assumed PF duties; initiating a slow climb to 2;500 with the student assisting as PM monitoring engine indications and verifying cruise switch positions. The aircraft was turned back toward ZZZ; the PF contacted ATC to report engine roughness and requesting vectors to ZZZ; then requesting and receiving the visual approach to XX. The PF requested the PM to assist with the QRH and the passenger (back-seating student) to assist with monitoring engine indications. ATC asked whether the PF wanted to land on RWY XY or RWY XX; with the PF selecting RWY XX. The PF contacted ZZZ tower and received clearance land on RWY XX. The left engine continued surging and developing partial power; the PF elected to not conduct a full shutdown; and landed safely on RWY XX. During taxi back to the ramp and while on taxiway 1 the left engine stopped running.