If a person is on a life support system due to the failure of one or more organs and not able to return to normal life without them again, if the family consents to the doctors' recommendation to turn off the artificial life support, can this be considered encouraging to kill, violating the first precept?
No it is not killing. Because there's no intention of killing. You just stopped doing things to sustain his life. It doesn't even have to be a relative. So many people die due to famine all over the world. So many animals are being slaughtered every day. You could stop everything you are doing right now and go and try to save them with all your time and money. But by not doing that, are you killing those whom you might have saved? No! Not doing a good deed isn't necessarily doing a bad deed.
But if there's the intention of killing, turning off the switch breaks the 1st precept.
Here's an article (found using Google) about that, Letting-Go or Killing: Thai Buddhist Perspectives on Euthanasia which (being Thai) I presume is Theravada.
It mentions several real considerations, including,
[...] They also recognize that sometimes in real life human choices are only between two evils. Yet even in this tragic life situation one still has responsibility to choose the lesser evil. But for such agonizing decisions there has been little guidance culled so far from Buddhist sources to help Buddhists and to ease their conscience. As generally known, Buddhism encourages each person to face the troubles by relying on oneself alone, without expecting any divine power to intercede and help. [...]
It warns that,
To these lay Buddhists, questions are raised if when asked whether economic factor, the age of the patient and the quality of life would make any important difference in their decisions regarding the use of life-support systems, none could give a definite Buddhist answer. Some say yes and some no, but they could not find grounds in Buddhism to support their answers.
The reality is that some forms of euthanasia are currently being practiced in some hospitals by doctors who make life and death and decisions alone without any directives whether these be ethical, religious, moral or legal.
Perhaps the Buddhist concept of mutual dependency and interrelatedness (paticcasamuppada) should be applied to the field of medicine. This concept affirms the interdependence of all beings.
Apart from this, while keeping their primary image as healers, dedicated to preserving and prolonging the life of all patients under their care, they have to develop a new approach to death and dying, so that when death becomes imminent they would become graceful acceptors of the inevitable, without considering the hopeless condition of the dying patient as representing the failure of their skills and knowledge. They should instead turn their full attention now to the compassionate care of the dying. Their main concern of course is to relieve the suffering of patients and families and ensure a "good death".
FWIW, in the cases where my family has died (or been allowed to die) in hospital, I viewed that as their being killed by the disease/illness, and not as their being killed by their doctors.
It can also be helpful if they, who were dying, let you know in advance what/how much medical intervention they want.
First of all Buddhism is against killing and that includes so called "Mercy killing". As lord Buddha once said every being at any condition likes only to live. No matter whether it's killing, ordering to kill, approving killing, or advising killing, it is not approved in Buddhism, even when we are talking about a person in extreme pain or a bad condition/Coma.
Please refer "Meththanisansa sutra"