Cry. That's it. That's all you can do.
Okay, I'm being dramatic, but there's really little you can do when you reach the end of a work in progress.
If you're on AO3, you can subscribe to the work in order to get notifications when the author posts a new chapter and check the author's notes to see if they have a set posting schedule. You can leave comments letting them know how much you enjoyed the chapters you've read so far and would love to read more when they get a chance to post again. You can give the work Kudos to really drive home how much you loved it.
But what you should not do is harass the author to get them to post quicker. As a fanfiction writer (sort of), I can tell you that encouraging and happy comments always motivate an author to write and post quicker than angry comments do.
I recently posted a fic for the first time in years because I was inspired by one of the last "Game of Thrones" episodes and needed to get the oneshot out of my head. I've gotten a fair number of kudos and comments on it, which has actually motivated me to work harder on a WIP I had started than I had been. I decided to try to finish the WIP before I start posting chapters because I remember, when I used to post WIPs, the amount of negative reaction the long stretches between chapters got.
I haven't worked steadily on a WIP I intend to post since high school. Back then, when I wrote 1D het fanfiction, I had a decently popular work that I tried to update as often as I could, but with school, work and a personal life, I didn't get to write it as often as I would have liked.
I still remember one girl who posted multiple comments on the work, yelling at me for leaving my readers hanging for a couple weeks at a time. She basically said that I shouldn't write fanfiction if I couldn't commit to updating because my readers deserved better.
All her comments made me want to do was stop writing the work altogether. What can I say? I'm a petty bitch sometimes. But instead, in a move much pettier than abandoning my work, I posted a "joke" chapter with some completely ridiculous scenes and dialogue, ending it all with the main character waking up and realizing it was all a dream and that she lived in the real world where people had more pressing issues than writing fiction about boybands. Yeah, she didn't like that.
I ended up finishing the fic, but it wasn't because of that girl or the other mean commenters, it was because of the other people who commented telling me to take my time with each chapter, not to listen to the negative people.
So, if you find yourself at the end of a WIP with nowhere to go, just know that the author doesn't owe you anything. They don't owe you more chapters or an ending or justification for their posting schedule. There are more than a few WIPs in my AO3 subscription list that haven't posted in weeks, but here I am, minding my own business and not harassing strangers online because I think they have wronged me somehow.
If you don't think you can handle waiting weeks between chapters, maybe reading WIPs isn't for you. That's why the "Completion Status" field of AO3's search is such a godsend. Just check that little box and voilà, a whole slew of fics that have endings for your enjoyment.
But if you're out of complete works that interest you for your pairing and need to take a step into the WIP world, just remember my tips above. And another piece of advice: You can specify in an AO3 search that you only want to see WIPs that have been updated within the past month (or however long ago), and that way, you will only be shown WIPs that are still being updated rather than accidentally falling victim to a fic that was abandoned in 2014.
What do you do when you come to the end of a WIP? Are you a writer of a WIP? Do you find yourself motivated more by positive or negative comments? Have you ever been petty about a mean commenter like me?