Are students who are asylees eligible for National Science Foundation (NSF) grants? Are graduate students who are asylees pursuing a doctorate able to apply for funding from the National Science Foundation?

According to the proposal preparation and submission guidelines (part E):


  Graduate students are not encouraged to submit research proposals, but should arrange to serve as research assistants to faculty members. Some NSF divisions accept proposals for Doctoral Dissertation Research Grants when submitted by a faculty member on behalf of the graduate student.


The guideline also says that one category of applicants for funding are:


  Institutions of Higher Education (IHEs) - Two- and four-year IHEs (including community colleges) accredited in, and having a campus located in the US, acting on behalf of their faculty members.


Does this mean faculty can apply for NSF funding through their academic institution for a student who has been granted asylum but is not yet a permanent resident?
That's a great question to ask the NSF directly, but generally everything the NSF does distinguishes people only by the following categories:


Their position in their career. For example, some programs are only available to graduate students, to early career faculty, etc.
Their citizenship status. Some programs are only available to citizens and  permanent residents, but not others.


I have never seen a distinction based on the exact non-citizen (non-permanent resident) status. That would mean that it doesn't matter whether you are a student residing legally in the US because you have an F-1 visa, are an asylee, or are in the country through any other legal means.

(I will say that just because I haven't ever seen such a distinction doesn't mean that it doesn't exist. But I suspect the NSF doesn't care about these things.)