Bad person who got banned had address X.X.X.X
Bad person who got banned released this address via his machine being off long enough or discontinuing service, or the ISP resetting it or some other possibility...

You possibly live near/in same ISP segment as Bad person.... and when your Dialup/Cable Modem/DSL refreshed its IP address, it picked up Bad person's IP address.

Just if you needed a little more explanation /hides now.

If you're using Dialup, you would easily be able to reconnect and likely get a different IP address.
If using Cable/DSL, sometimes these IP addresses are kept for days, weeks, or months, depending on the uptime of all the hardware involved..... or forever if its statically assigned... which most don't that I know of.