The way I see it is easily illustrated with a simple analogy. You have self ownership of your own body. Imagine all of your property, including your body, being represented by a deck of cards. One card represents your ownership of your car, another your house, another your body, etc. etc. You have the right to trade these cards with other people, or throw them on the ground and abandon them. By attempting suicide you are throwing the card that represents your ownership of your body on the ground. At this point anyone else is free to either pick it up, or abandon it, etc.
You have the right to attempt suicide, but by throwing that card that represents your life on the ground, you are giving anyone else the right to pick up that card and take possession of it, and take control of your body. So if I were to witness someone attempting suicide, I would have the right to pick up that card, and take control of that property, and morally I feel that I would be obligated to help restore it to its full value and return it to its original owner.
In practical application that's throwing a suicidal individual into the mental ward of a hospital where they can be nursed back to sanity by well trained and caring staff, which is something that I have had the honor and opportunity to assist with in the past.