  The Swampland Cobordism Conjecture successfully predicts the supersymmetric
spectrum of 7-branes of IIB / F-theory. Including reflections on the F-theory
torus, it also predicts the existence of new non-supersymmetric objects, which
we dub reflection 7-branes (R7-branes). We present evidence that these
R7-branes only exist at strong coupling. R7-branes serve as end of the world
branes for 9D theories obtained from type IIB asymmetric orbifold and
Dabholkar-Park orientifold backgrounds, and an anomaly inflow analysis suggests
the existence of a gapless Weyl fermion, which would have the quantum numbers
of a goldstino. Using general arguments, we conclude that different kinds of
branes are able to end on the R7, and accounting for their charge requires
exotic localized degrees of freedom, for which the simplest possibility is a
massless 3-form field on the R7-brane worldvolume. We also show how to
generalize the standard F-theory formalism to account for reflections.
