  Let R be a commutative noetherian local ring, and let X be a resolving
subcategory of the category of finitely generated R-modules. In this paper, we
study modules in X by relating them to modules in X which are free on the
punctured spectrum of R. We do this by investigating nonfree loci and
establishing an analogue of the notion of a level in a triangulated category
which has been introduced by Avramov, Buchweitz, Iyengar and Miller. As an
application, we prove a result on the dimension of the nonfree locus of a
resolving subcategory having only countably many nonisomorphic indecomposable
modules in it, which is a generalization of a theorem of Huneke and Leuschke.
