Asylees are refugees who are at a land border or point of entry in the US. According to INA §208(a), asylees must qualify as refugees, meaning that they have to prove a well-founded fear of persecution based on a protected ground. Persons interdicted in the high seas may not qualify for asylum.
The person’s nationality has to be determined before asylum can be granted. Like in Urgen v. Holder, 768 F.3d 269, 272-74 (2nd Cir. 2014), where statelessness alone is not enough to qualify for asylum. But if statelessness is the basis for persecution, then it qualifies, such as in Stserba v. Holder, 646 F.3d 964 (6th Cir. 2011).