Grad students and postdocs often leave a lab with unpublished data. Often, when the work is eventually published the author list is not what was anticipated. This can cause hurt feelings and if someone was really counting on those first author publications coming through, career progression. At the same time it is important to recognize that by leaving you give up control, and a paper coming out with you included as a more minor author than expected  is much better than no paper coming out at all.  How do you manage your own expectations and set yourself up for success? As with many things, it depends. In this case, it depends specifically on 1) where your data and writing are when you leave and 2) how involved with the project and your former lab you remain, which is often not fully within your control. Simply put, the closer to the work is to its final publish form and the more involved you remain throughout this process the more likely you are to end up retaining sole first authorship.

Scenario 1

You are PI of an established lab One of your graduate students defended and submitted a key portion of their thesis work to a journal. The manuscript is reviewed, and it requires a lot of revisions to the text, how the data were analyzed, and more experiments. The first author, your former graduate student, has moved across the country and is busy getting their postdoc project started. They’re getting settled in a new place, applying for fellowships, and getting started with new techniques in a new subfield. You converse, and both think that it will take around 6 months for someone to complete the required experiments. Your former grad student’s postdoc advisor expects them to work on their current projects, and your current students are all busy with their own projects. Six months is a lot of time, and the only thing you can offer to get someone to spend the time is authorship.

Scenario 2

The paper comes back with positive reviews, and only requires one fairly straightforward experiment. Your former grad student says they'll get the experiment done, so you send them supplies. As is often the case, it takes significant time to get the experiment up and running and weeks go by. You contact the grad student and get updates. Eventually the data arrive, but so much time has elapsed that advances in the field require significant portions of the text to be rewritten. The former graduate student hasn't kept up with the field, as they've moved on to their new project. A postdoc offers to do the rewrite and does a great job placing the data within the context of all the new information that has been published in the field. Without their rewrite, the paper would not have been published.

Scenario 3

A grad student leaves with the last chapter of their thesis unpublished. They promise to work on it and have it ready for submission soon. A new student picks up the project, planning to build on it in a new direction. They make substantial progress and want to publish their work, but can't because it relies on the previous student’s unpublished data. You contact your former grad student who assures you they are working on it, but can't give a firm date as to when the manuscript will be finished. Plus, they have fellowship deadlines looming, which take priority. The new grad student offers to draft the manuscript. 

Outcome

I think you can see where I'm going with this. In all scenarios, the original grad student did the bulk of the work leading to the manuscript. Because publishing takes a long time, something changed that made them unable to complete the process within time constraints. Someone else steps in, and the paper only gets out because of their efforts. The PI has to decide- do they get first authorship? Co-first? Second? What if the person stepping in only agrees to do so if they can share first authorship? They too have a timeline.

The only way to guarantee you'll get sole first authorship of your publications is to stay in your lab until the papers are fully published. This isn’t always possible, and even if it is, the time spent not progressing your career is something you have to weigh against the benefits of the authorship.