It would be nearly impossible for this question to ever happen actually in the world of reality. How in the world would such a thing happen. It goes against some of the most basic things that makes one even human in the first place. At the very least a person would be selfish once.
No I don't think that humans can lead an entirely unselfish lives if we did we wouldn't have a religion because you would just have everyone selflessly living and caring for each other. It is almost impossible for one to lead and entirely unselfish life when living in the real world
I don't believe that is it possible for man (humans) to lead completely unselfish lives. By our very nature man always has his self-interest at the forefront. I do believe that it is possible for humans to act unselfishly a majority of the time, but not ALL of the time.
Selfishness is like any other trait: only a vice if carried to extremes. Altruism can also be bad when carried to such an extreme as to be self-destructive or unnecessary martyrdom.
As common wisdom says, it's impossible to help others if you can't help yourself. People have to be selfish enough to say "I can't give anymore" when they can't. It's both healthy and responsible to the people who are asking for help. They know they need to look elsewhere instead of counting on someone who is on the edge of collapse.
A good example of the importance of a little selfishness is people who can't say no. They know well how destructive trying to be totally unselfish can be. Being the go-to helper seems like a noble endeavor until the constant sea of commitments begins to kill them, often literally. By the time they're at the place where they're ready to finally start saying no, they've usually angered and disappointed others and run themselves close to a nervous breakdown.
I do not believe that humans can live entirely unselfish lives. There are people who are generous and are not selfish very often, but we have a human nature that will eventually get in the way and tell us that we need to worry about ourselves first. It is necessary for survival.