In reply to mateocaramessaddler:
They mostly coordinate some suitable people to come get you, treat you and bring you out. How well they can do that depends where you are and what resources are available for them to make use of.
KT (and Lenin, to some extent) is unusual, compared to Himalayan or Karakoram peaks, in that there are helicopter flights going in and out all the time, so if they can get you off the mountain, then a helo flight back to a hospital is not such a big thing - like it would be in Pakistan. There was a helo sitting at BC most of the time I was on Lenin, but I only saw it fly once.
Whereas in Nepal, if you have an accident on a big mountain and call a rescue, there is a chance that a helicopter will come and rescue you from ON the mountain, even above 6000m, and take you straight back to hospital. This will not happen on KhanTengri or Lenin as those big Russian Mi-8 helicopters won't fly up onto the mountain like the rescue helos in Nepal.