It's OK to eat old celery as long as the celery is not actually spoiled.
Celery can naturally go limp when stored in the refrigerator and if the celery is just limp or is turning a slightly different color then it's still okay to eat the old celery.
Just make sure there's no mold on the old celery and no bad smells to the old celery.
If the celery does smell bad or has a bad taste to it then it's bad and should not be eaten.
If the celery has a bit of mold on it you can break off or cut off the moldy part of the celery and eat the rest of the celery.
When celery is spoiling or going bad the bad or spoiled celery will typically become soft, and discolored and become easy to bend.
If in doubt about the old celery being too bad to eat then throw it out to avoid getting sick.