I am a fresh mathematics Ph.D who has begun a three year postdoc at University X. I applied for an NSF postdoctoral grant last year with University Y (with Y not equal to X) and did not get it. This year I want to re-apply. I like where I am and so I am planning to apply for the NSF with a mentor at University X. I have two questions.
Are there examples of a postdoc at an institution being awarded an NSF grant to stay at that institution (before their postdoc runs out)?
Are there any particular pitfalls I could find in applying at an institution that is already planning on paying me for three years? That is, if the NSF funds me then the job market "lost" a job in the sense that my postdoc position won't be replaced by my institution.