Insofar as I can determine, neither the Hebrew Bible or the New Testament deal with suicide per se. During the Middle Ages, the Western Church (at least)developed a teaching regarding those who committed suicide. The theory argued that to take one's own life was to usurp God's rightful place. In a sense, suicide came to be regarded as a kind of rebellion against God that left no opportunity for repentance. The practice of denying burial on holy ground to suicides dates from this era as well.
In my experience, I find most Christians have not studied the matter. Instead, they've picked up on the medieval concept via movies, popular literature and conversations with friends.
My personal perspective is that the medieval position is unbiblical. It caters to our desire to judge others, a desire Jesus warned us to resist: "Judge not."
When we separate theology-making from a pastoral connection with living and dying persons, heartless logic often replaces love as the guidestone of theology. It seems to me that God's love/grace is sufficient to cover the kinds of pain which may lead to suicide. The church's task, then, is to comfort the bereaved and commend the departed into God's hands.
Your story about the student connects with my own experience as a pastor and a human being. My reponse to him would be the same as I give to others in such a circumstance: "Your loved one is in the hands of God, who is gracious. I suspect the two of you will meet again in the presence of God, where you will find your friend fully healed and filled with new life."
God's grace, rather than questions about human intentions, is the foundation on which my position rests. The practical result, though, is that it seems the rabbis and I once again have found our way to common ground.
Like many Christians, I reject active euthanasia. To intentionally take a human life crosses a line I do not think the Bible allows us to cross. Passive euthanansia, on the other hand, may well be an act of faith. We may choose to trust God, accept our life is coming to a natural end, and refuse medical procedures that may stretch our living days without providing an ounce more of real life. This amounts to saying, "Into your hands, I commit my spirit."
What else would you like to say about the Sixth Commandment? Are we ready to move on to the Seventh Commandment?