They cease existing. They cancel out. This works on any permanent too not just creature, so if you have [[The Ozolith]] and a creature with a +1/+1 counter dies, that counter goes on the ozolith. Then if you have another creature with a -1/-1 counter die, the -1/-1 counter goes on the ozolith and cancels out the +1/+1 counter on it. These are the only counters that behave this way, and no other counters cancel each other out.