The parent species can only get subspecies appended if it is a polytypic species, but you can still refer to it by the binomial Genus species without having to indicate subspecies. Conversely, a monotypic species is only ever referred to by Genus species (because it doesn't have any subspecies).
It does indeed help to have a concrete example. I understood before that the species was the container for all the subspecies. What I didn't know if, as in the case you used, the formerly monotypic species had to have a subspecies appended or if it could remain a binomen. (Thank you, @l_raty for the terminology.) It makes logical sense or otherwise referring to Puffinus puffinus and meaning only the Canadian form would not be clear.
Are you asking: when a formerly monotypic species has a new subspecies named, which population becomes the nominate (receives the same name as the species name)? If so, then the answer is: whichever population is the one that was originally named becomes the nominate subspecies. That is to say: in the original description of the species, the population that is the source of the holotype specimen is the one that is considered "nominate" and any other new taxon named that falls under that species name receives its own subspecies name. So, for example, Great Gray Owl was first described in 1772 from Hudson Bay, Canada, and its name is Strix nebulosa. However, when a new subspecies from Scandinavia was named "lapponica" in 1798, the American form then became "Strix nebulosa nebulosa" as it was the first named and is thus the nominate subspecies. But the type locality (the place from where the holotype specimen comes) isn't always the place where the nominate population lives, as holotypes can be migrants or even vagrants, so the type locality may not be representative of the regular distribution of that named population. It is the source population of the holotype that is the one properly labeled by that name.
