PA34 INSTRUCTOR PLT WAS CONDUCTING TRAINING FOR THE LOSS OF PWR ON ONE ENG DURING TKOF. THE STUDENT PLT FAILED TO REACT BY REDUCING PWR; AND THE ACFT DEPARTED THE RWY.

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PURPOSE OF FLT WAS TO CONDUCT A COMMERCIAL PLT MULTI-ENG LAND INITIAL RATING END-OF-COURSE STAGE CHK. FLT WAS UNEVENTFUL AND STUDENT WAS DOING WELL. NEAR THE END OF THE STAGE CHK WE LANDED AT ZZZ TO CONDUCT THE REQUIRED LNDGS. AFTER THE FIRST LNDG WAS COMPLETE; I INSTRUCTED THE STUDENT TO TAXI BACK FOR TKOF. DURING THE TKOF; AS THE STUDENT WAS APPLYING TKOF PWR; I GAVE HIM A PARTIAL PWR LOSS ON THE R SIDE (#2) ENG. THE STUDENT FAILED TO REDUCE PWR ON BOTH ENGS AND INSTEAD CONTINUED TO APPLY FULL PWR ON THE L ENG. I IMMEDIATELY CALL FOR CTL OF THE ACFT. BY THE TIME CTL WAS RELINQUISHED; THE ACFT WAS HEADING TOWARDS THE EDGE OF THE RWY. IT WAS MY DECISION THAT IT WAS SAFER TO EXIT THE RWY AND STILL KEEP THE ACFT ON THE PAVED SURFACE; THEN STRAIGHTEN THE NOSE. IT WAS MY OPINION THAT IF I HAD REMOVED PWR FROM THE OTHER ENG AND TRY TO STRAIGHTEN THE ACFT; WE MAY OR MAY NOT HAVE HIT A RWY EDGE LIGHT. AFTER BRINGING THE ACFT TO A COMPLETE STOP; WE RELOCATED THE ACFT BACK ONTO A TXWY AND CHKED FOR DAMAGE. NONE WAS FOUND AND THE DECISION TO RETURN TO HOME ARPT WAS MADE. THE STUDENT LATER INFORMED ME THAT HE HAD NEVER BEEN TAUGHT THE ENG FAILURE ON THE GND PROC AND THOUGHT THAT MAYBE ONE OF HIS BRAKES HAD FAILED.