If a person stops contributing to a project do they deserve authorship?
That's always an awkward situation. The bar to &quot;deserve&quot; authorship is generally considered to be pretty low: If you intellectually contributed to the project, you should be a co-author. At the same time, people generally have the expectations that all co-authors continue to contribute to the paper in some form or other till the end, for example through the writing and proof-reading process.
So if someone helped develop an algorithm or worked on produce the data for the paper, they probably should be a co-author. But it is not unheard of to write an email to them and say

As an author, there is also an expectation that you continue to work with us on writing the paper; I recognize that you have moved on in your career, and if you feel like you don't want to be on the paper because you don't have the time to work on it, that's ok with us as well.&quot;

That's an awkward email to write, but sometimes it's necessary to either get a person to contribute more, or remove themselves from the paper.