  Non-trivial topology and unconventional pairing are two central guiding
principles in the contemporary search for and analysis of superconducting
materials and heterostructure compounds. Previously, a topological
superconductor has been predominantly conceived to result from a topologically
non-trivial band subject to intrinsic or external superconducting proximity
effect. Here, we propose a new class of topological superconductors which are
uniquely induced by unconventional pairing. They exhibit a boundary-obstructed
higher-order topological character and, depending on their dimensionality,
feature unprecedently robust Majorana bound states or hinge modes protected by
chiral symmetry. We predict the 112-family of iron pnictides, such as
Ca$_{1-x}$La$_x$FeAs$_2$, to be a highly suited material candidate for our
proposal, which can be tested by edge spectroscopy. Because of the
boundary-obstruction, the topologically non-trivial feature of the 112
pnictides does not reveal itself for a bulk-only torus band analysis without
boundaries, and as such had evaded previous investigations. Our proposal not
only opens a new arena for highly stable Majorana modes in high-temperature
superconductors, but also provides the smoking gun evidence for extended s-wave
order in the iron pnictides.
