Hi Customer (name blocked for privacy),
The part of the tail that fell off was injured, and died.
If the skin over the end completely covers the bone of the tail, it may be satisfactorily healed. If not, expect it to be bothering him. It would need to have the bone at the tip removed and the skin properly closed over it. But, even if it appears so now, keep an eye on it, and him in general for another few weeks.
If he appears to be off his appetite, or not quite himself, or if his tail appears to be bothering him, like chewing at it or chasing it too much, you should have him, or it examined more closely by his vet...
I hope this is helpful. Best wishes.
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