  We study the possible signatures of prethermal strong Hilbert space
fragmentation (HSF) for one-dimensional (1D) fermions subjected to a periodic
drive. We extend the results of Phys. Rev. Lett. 130, 120401 (2023) to show the
possibility of such fragmentation for a large class of experimentally relevant
drive protocols. Moreover, we demonstrate the persistence of HSF when the
fermion chain is taken away from half-filling. Both these analysis indicate the
robustness of the fragmentation phenomenon reported earlier. We also provide an
alternate derivation of the Floquet Hamiltonian of the driven chain which
yields insight into the generic nested commutator structure of its higher order
terms. Finally, we study the density-density out-of-time-correlators (OTOC) of
the driven chain both away and near the special drive frequencies at which its
first order Floquet Hamiltonian exhibits fragmentation. We show that these
OTOCs, for a chain with open boundary condition, exhibit a distinct periodic
unscrambling of information at special drive frequencies; such unscrambling can
therefore serve as a marker of prethermal HSF. We provide an approximate
analytic explanation of the role of HSF behind such periodic unscrambling and
discuss experiments which can detect signatures of strong HSF in such driven
chains.
