  Following Elliott's earlier work, we show that the Elliott invariant of any
finite separable simple $C^*$-algebra with finite nuclear dimension can always
be described as a scaled simple ordered group pairing together with a countable
abelian group which unifies the unital and nonunital, as well as stably
projectionless cases. We also show that, for any given such invariant set,
there is a finite separable simple $C^*$-algebra, whose Elliott invariant is
the given set, a refinement of the range theorem of Elliott in the stable case.
  In the stably projectionless case, modified model $C^*$-algebras are
constructed in such a way that they are of generalized tracial rank one and
have other technical features.
  We also show that every stably projectionless separable simple amenable
$C^*$-algebra in the UCT class has rationally generalized tracial rank one.
