Even going to 0 hit points without any healing would not end any conditions that are put on you (as you are not DEAD at that point, only dying). For example, if you are poisoned in an adventure and are taking ongoing 5 poison damage, and an enemy hits you, taking you down to 0 HP, you will still continue to take the ongoing 5 poison damage until either A) you die, b) you make a save (if allowed) to end the ongoing damage, or c) the time limit (on any ongoing damage that doesn't allow a save) expires. C would be most common for non-damaging effects like dazed, stun, etc.
More specific example:
Lets say that your character is attacked by a fighter and is marked. That mark lasts until the end of the fighters next turn. Then, in the same turn, a warden comes over and uses a free action to mark you and others around him. Now, unless the fighter has used an effect that stated that his mark cannot be superseded, the WARDEN's mark is now what takes effect.
If on that same turn you were hit by the warden, and dropped to -2 HP, you would still have the mark until the end of the Warden's next turn. If your cleric ally healed you and you were back up to 14 HP (arbitrary number) in that same round, then you are STILL marked by the Warden.
Hope that helps!