  Topological quantum matter exhibits a range of exotic phenomena when enriched
by subdimensional symmetries. This includes new features beyond those that
appear in the conventional setting of global symmetry enrichment. A recently
discovered example is a type of subsystem symmetry fractionalization that
occurs through a different mechanism to global symmetry fractionalization. In
this work we extend the study of subsystem symmetry fractionalization through
new examples derived from the general principle of embedding subsystem symmetry
into higher-form symmetry. This leads to new types of symmetry
fractionalization that are described by foliation dependent higher-form
symmetries. This leads to field theories and lattice models that support
previously unseen anomalous subsystem symmetry fractionalization. Our work
expands the range of exotic topological physics that is enabled by subsystem
symmetry in field theory and on the lattice.
