In previous Star Wars films lightsaber duels with a clear winner ended in one of two ways, death or dismemberment for the loser. In The Force Awakens Finn was slashed by Ren, falls unconscious and remains so for the rest of the film. What exactly happened to Finn?
Finn suffered a substantial cut to the shoulder and a slashing wound to the back (his chest in the novel) as well as multiple soft-tissue injuries and a punch to the face. Although the major wounds were evidently cauterised by the lightsaber, he would still have likely gone into shock from the extent of the trauma
Advancing relentlessly, he was driven by something that Finn could not even sense, far less counter. Still the ex-trooper fought back, until Ren landed a blow that cut across Finn’s chest and sent the lightsaber flying from his hand.
Below them, Rey huddled beside the unconscious Finn. Turning him over, she recoiled from the wound Ren had inflicted with his lightsaber. The blow had cauterized instantly. In the dim light she couldn’t estimate its depth, nor if it had passed through any vital organs. Holding the unresponsive body in her arms, she started to cry. There were worse ways to die, she told herself as the ground continued to shake and trees began to topple around her.
After his rescue, he was placed into a medically induced coma to allow him to recover more fully.
Within the intensive care pod in the medical center, Finn lay in a medically induced coma, his health and life still very much in the balance. Dr. Kalonia’s prognosis had been favorable, even positive, but nothing certain could be said until Finn had fully recovered. When wholly parsed, the phrase “be all right” could mean one thing to a physician and something else entirely to the patient.
All quotes from Star Wars: The Force Awakens - Official Novelisation
There has now been positive confirmation that Finn's injuries were not life-threatening and that with a bacta dip, he'll be as right as rain, just in time to star in the sequel.
Finn had a nasty encounter with a lightsaber during his duel with Kylo Ren. Luckily, it seems Kylo didn’t hit anything vital, and with the help of a suit full of healing bacta, Finn should be up and about in no time. He’s going to wonder what has happened to Rey in his absence