  We construct a sheaf-theoretic analogue of the wrapped Fukaya category in
Lagrangian Floer theory, by localizing a category of sheaves microsupported
away from some given $\Lambda \subset S^*M$ along continuation maps constructed
using the Guillermou-Kashiwara-Schapira sheaf quantization.
  When $\Lambda$ is a subanalytic singular isotropic, we also construct a
comparison map to the category of compact objects in the category of unbounded
sheaves microsupported in $\Lambda$, and show that it is an equivalence. The
last statement can be seen as a sheaf theoretical incarnation of the
sheaf-Fukaya comparison theorem of Ganatra-Pardon-Shende.
