As @eobox91103 said, if you are fortunate enough to join a swarm before the torrent gets deleted and there are still others in the swarm then by all means keep the torrent running in your client. When the torrent gets deleted from the tracker it seems that anyone already in the swarm can continue to both upload and download. As such, as long as there is a full copy available, either from seeders or from enough leechers, it is still possible for the download to finish. I've managed to complete a few downloads in the past after they became unregistered. If you are lucky enough to have the full copy then please do keep it running as long as there are any leechers in the swarm. You won't get credited for the upload on the site, but you will save people from having wasted a lot of ratio on a download they might never have been able to finish.

If a torrent is taken down (i.e., shows up as unregistered), the Great Tracker stops being a matchmaker. But if you're already connected to someone who has data you want, or needs data you have, that connection will usually stay active and data will flow one way and/or another, but it won't be seen by the tracker and won't influence your ratio.

Even if you haven't fully leeched all the data from a torrent that's taken down, it's worth keeping it active in your client to see if there are bits out there that you can get from existing connections. Similarly, if you have a completed torrent that's been taken down, I like to keep it active in my client to that others who are already connected to me can still get the data they're missing. I won't get "credit" for it, but it's a nice thing to do.

What about uploading and downloading that occurred before the torrent was deleted?

@serenity no, because you're not uploading anything to anyone since the torrent doesn't technically exist.

Essentially true..

Technically, while you may actually be uploading or downloading data (because those are site-to-site connections - without involving the tracker or the site), when that UL or DL data gets reported to the tracker, there is no torrent to assign it to, so it doesn't count - in either direction.