> If it keeps coming back it's not eliminated is it?
Yes it is eliminated. If it's not eliminated, it can't come back.
If someone removes all the rats from the house, so that there aren't any, we say they have eliminated the rats.
If, later, someone brings a rat to the house, we say they have brought rats back to the house and now we need to eliminate them again.
Elimination is an action, the action of removal, and eliminated means the removal is now done. It means the thing is gone. It can still come back later.
If your house has rats and you call an exterminator, you don't say you still have rats because other houses do and they might show up again.