In many countries there are funding sources that enable students or postdocs go study or work at a university of their choice, usually abroad. Usually for these applications, the applicant has to get in touch with a potential supervisor to get a letter of invitation and approve their research statement. More often than not, the potential supervisor is expected to discuss the ideas in detail, and also help improving the cover letter and research statement, since the award of the fellowship depends on it.
I have noticed the following situation recently: students from abroad approach me with interest to do research in my lab, and ask for help in checking their application and aligning ideas to my research. We have a call or two, we discuss the details, we come up with a strong application (that looks much better than the one they initially approached me with). As the application deadline approaches I don't hear back from them anymore nor they respond to emails. Soon I learn that in parallel they approach a more famous lab with a much better application (thanks to me). Since the cover letter and research statement are now of high quality (for someone at that stage in their career), they are accepted easily, and get funding (sometimes directly from the lab).
This is new to me, and in just a short period of time I had three similar cases. I spent at least a day on each (calls, emails and checking the application), so it is a waste of time, and frustrating.
Is this a new trend? What is the best way to avoid this, while not discouraging genuine applicants?