FiMFiction is littered with stories marked CANCELED or ON HIATUS (and let's face it, the latter means the former so often that most readers see the two as synonymous within the realm of fanfic). It's also littered with stories marked INCOMPLETE, which haven't updated since 2012.
There's absolutely nothing unexpected about any of that. As long as fanfiction is a (nearly) zero-barrier-to-entry, (mostly) remuneration-free field, authors will get in over their heads, start something they don't know how to finish, or just run out of the time, energy, or interest needed to finish their stories. Abandoned stories aren't a problem that needs to be fixed...
...But it sure would be nice if authors could all agree to a few simple bits of etiquette as regards them. My suggestions, below the break.
1) Don't promise more than you can deliver
So, you've written the first thousand words of your epic tale, one which will span continents, centuries, genres, and anything else you can measure numerically. Good for you!
Now, personally, I would advise writing a bit more (okay, a lot more) than just those first thousand words before hitting submit, but this post isn't about advice, it's about etiquette. If you're only posting those first thousand words to "test the waters"--if you're planning on dropping this idea if it doesn't catch on with readers, say--be up-front about that. Put it in the description, or in an author's note at the start of the story. Give your prospective readers fair warning that they're getting on a ride that's subject to immediate cancellation.
Or say it's taken you three months to get those first thousand words on the page. I know it's tempting to put "Updates every week!" in the description--and I'm sure you're planning to keep that promise. But be wary of making promises you don't know you can keep. Unless you've previously demonstrated that you can write at that pace, don't claim you'll deliver something at certain intervals only to fall short immediately.
2) Don't give people false hope
This is challenging, because often the author isn't lying to his readers when this happens--often, the author is lying to himself. But seriously: if it's been two years since you last updated, you can come back to the story and publish a new chapter. You almost certainly have readers who would be thrilled to have that happen, in fact. But this is not the junction to make a "hey guys, finally getting some work done on my story again!" blogpost. At this point, unless you actually have a completed, edited, whatever-ed chapter ready to go up, don't promise anything. Even if you have absolutely pure intentions (and again, I think most authors do in this situation), you're basically stringing readers along with this kind of thing. They'll come back if/when there's a new chapter; don't try to hype them up when there's still any chance--which, whether you admit it to yourself or not, usually means "a very good chance"--that this is a false alarm.
3) Dead fics suck, but they're better than Schrodinger's fics
A lot of times, an author won't want to switch their story from incomplete to on hiatus (or cancelled) because they don't want to disappoint their readers. That's totally understandable, and even laudable. However, if you know deep down that you're never coming back to a story--or, in the case of the on hiatus tag, that you won't be coming back to it for at least a few months--there's value in closure. Readers will almost certainly be disappointed to see those tags coming out, but it's a lot easier to deal with than for those same readers to be clicking over to your profile every few months, seeing if you're still around and wondering whether they'll get some more of their story some day.
Nobody is saying that you have to have an itchy trigger finger with these thing, mind you. But, if you know a story is dead or in the closet, don't withhold that knowledge from readers. Let them know as soon as you know: it's the polite thing to do.
4) Learn something from the experience
This is the biggest one for me. Many fanfic authors have abandoned an in-progress story at some point--I know I have, though that was back before ponies. But some people do it over, and over, and over. At a certain point, this kind of serial fic-abandoning starts to reflect poorly on the author.
When you have to give up a story for whatever reason (unless it's because you're never going to write any sort of fanfic ever again, I guess), do a postmortem. Figure out what went wrong that stopped you from finishing. Think about if there's something you can do differently next time, if there is a next time. Try to come away from your experience with some understanding of what you can do to make sure that the next story you write is one you can take to completion.
That last one's good etiquette, but it's also good authorial experience to look back and learn from when you've fallen short of your goals. Sometimes, good manners and selfish motives can come together.