  We study ${\mathcal N}=(1,0)$ six-dimensional theories living on defects of
non-geometric backgrounds of the $E_8\times E_8$ and the
$\text{Spin}(32)/{\mathbb Z}_2$ heterotic strings. Such configurations can be
analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau
threefolds. The majority of the resulting dual threefolds turn out to contain
singularities which do not admit a crepant resolution. When the singularities
can be resolved crepantly, the theories living on the defect are explicitly
determined and reveal a form of duality in which distinct defects are described
by the same IR fixed point. In particular, a subclass of non-geometric defects
corresponds to SCFTs/LSTs arising from small heterotic instantons on ADE
singularities.
