Some of us have lots of friends, some of us don't. But some simply don't have any. Sure, a teenager might have its parents, a woman might have her workmates and most have their family. Well, depending on how close you are with your family, parents or yout workmates, they may not be considered as friends. Friends are not only people you can laugh and have fun with, but they're also people you can cry to and tell your problems. And if you have no one to do all of those things together it's safe to say you don't have any friends.
So there is, in fact, people with no friends - therefore it is possible - but they're not necessarily healthy. Actually, I dare to say none of them are, at least according to what our society constitutes as healthy. Since we all live in a society, and that having friends is very common - if not an unwritten rule - a person without any feels not only lonely but excluded, left behind, not loved. That's why, besides the obvious, having people who cares about you (usually friends) is a necessity in order to be mentally healthy. Suicidal thoughts usually occur in the minds of those who feel isolated, like nobody cares if they're dead or alive, like they're not important.
And what makes us important? What gives us the feeling of being important, what makes all of our lives matter? People. Friends, precisely. Those special human beings who miss you when you're away, who laugh when you're near, who listen when you're sad. Only humans can make other humans feel important because your personality and character can only matter to those who can understand and apreciate them. That's the reason why we can't live alone, the reason why everybody needs friends. They are the ones who turn our life into something valuable. Because if nobody cares about us, then we might as well be dead.