  Future electron-proton collider proposals like the LHeC or the FCC-eh can
supply 1/ab of collisions with a center-of-mass energy in the TeV range, while
maintaining a clean experimental environment more commonly associated with
lepton colliders. We point out that this makes electron-proton colliders
ideally suited to probe BSM signatures with final states that look like
"hadronic noise" in the high-energy, pile-up-rich environment of hadron
colliders. We focus on the generic vector boson fusion production mechanism,
which is available for all BSM particles with electroweak charges at mass
scales far above the reach of most lepton colliders. This is in contrast to
previous BSM studies at these machines, which focused on BSM processes with
large production rates from the asymmetric initial state. We propose to exploit
the unique experimental environment in the search for long-lived particle
signals arising from Higgsinos or exotic Higgs decays. At electron-proton
colliders, the soft decay products of long-lived Higgsinos can be explicitly
reconstructed ("displaced single pion"), and very short lifetimes can be
probed. We find that electron-proton colliders can explore significant regions
of BSM parameter space inaccessible to other collider searches, with important
implications for the design of such machines.
