I re-watched the film. No screenshots yet but the very last film moments before the chasm opens show Ren lying on the snow, rising to a half-sitting position with his torso facing the screen square-on. His hand is clearly still attached and moving (he raises his forearm before raising the torso). He is clearly all in one piece and not dead nor Anakined.
The novelization says the following:
Kylo Ren's condition:
... Unarmed, he raised a hand and utilized the Force to fend off one slashing blow after another, until finally her fury penetrated his remaining defenses. Taking a glancing blow to the head and chest, he went down, a prominent burn slashed across his face. Weakened, he reached out toward his lightsaber, trying to draw it to him.
He was clearly alive, that wound doesn't sound terribly awful nor Anakin-style-limb-losing.
And Rey refused to finish him off. As we all know from Dark Helmet, evil will always win, because Good. Is. Dumb.
One downward cut, she saw. One quick, final strike, and she could kill him. The landing lights of a shuttle appeared in the distance, coming over the trees in her direction. She had to make a decision, now.
Kill him, a voice inside her head said. It was amorphous, unidentifiable, raw. Pure vengeful emotion. So easy, she told herself. So quick.
She recoiled from it. From the dark side.
So what happened to Kylo Ren then?
A deep gully formed, separating her from General Hux and the arriving troopers. Utilizing the tiny position sensor emplaced in Ren’s belt, Hux had tracked him to this spot. He would have taken Rey and Finn, as well, if not for the command that had been issued by the Supreme Leader. That took precedence over everything. There was simply no time left.
The two renegades were going to die here anyway, he told himself as he followed the troopers carrying Ren into the nearby shuttle. As soon as he was aboard, it lifted off, its occupants desperate to flee the dying planet.
So, they left.
Hux did that on Supreme Leader Snoke's direct orders, so Snoke clearly had further plans for Ren:
In the darkness of the cavernous assembly room, Hux stood before the image of Snoke. Try as he would, it was proving increasingly difficult to maintain a semblance of control.
“Supreme Leader, the oscillator is failing. The collapse has begun.” He looked downward. “There is nothing that can be done.”
Furious as he was, Snoke knew there was nothing he could do. So many plans so carefully laid, so many intentions that must now go unfulfilled…
“You will leave Starkiller at once and come to me with Kylo Ren. Leave immediately.” He added grimly, “It appears that he may have been right about the girl.”