http://support.chess.com/Knowledgebase/Article/View/16/13/how-do-ratings-work
And reaching 0 points is practically not possible, unless one refuses to play the game, and just resigns for the fun.
What happens when you hit 0 and lose a game? Nothing, you stay at 0.
explanation..
win games to get rating points! lose games to lose rating points!
the amount you win or lose depends on the difference between you and your opponent's rating.
in practice, it's pretty much not possible to reach 0 points :D
Easy, you play against someone stronger and if you win you get lots, and if you lose you lose little. Someone weaker and viceversa. About reaching the 0 points... i dont think thats possible. i have seen 700 elo players playing 1.a4 2.Ra3, completely new guys. so yeah, i dont think there is a even worse level.
And if you draw someone with a lower rating than you, you lose points; draw someone with a higher rating and you win points.
You win more/lose less points against an opponent rated higher than you; you win less/lose more points against an opponent rated lower than you because the higher rating is expected to be more likely to win.
Oh and anyway chess.com uses the Glicko system, not ELO.
Full explanation of Glicko: http://www.glicko.net/glicko/glicko.pdf
You need to be veeeeeeeeeeeeeeeeeeery bad chess player to have 0 elo :)
yeah, but we mean playing level, not a dumb guy that resigns and resigns to reach that "goal".
Many thanks to all of you and sorry to everybody if that might look like a silly question: I was just afraid to lose all of my rating points and be "banned" by the community 
!
Thank you for your thorough explanations: everything is clearer now!
Also, I was not aware of the Glicko-system, which seems to allow a much fairer playing!
Again many thanks, dear chess - mates: I hope to be able to play against one of you sooner or later!
Gemma
Kind friends,
I am new within the community, and I would be thankful if someone could explain to me how the elo-system works.
For instance, if I lost all of my elos (no surprise this is my worry: I am a novice of chess!), what would happen to my account? Could I keep playing games with elos? How could I manage to collect elos if I reached the 0 point?
Anticipated thanks to any of you who may be of help,
Gemma