  Composite states of electrically charged and QCD-colored hyperquarks (HQs) in
a confining SU(N_HC) hypercolor gauge sector are a plausible extension of the
standard model at the TeV scale, and have been widely considered as an
explanation for the tentative LHC diphoton excess. Additional new physics is
required to avoid a stable charged hyperbaryon in such theories. We classify
renormalizable models allowing the decay of this unwanted relic directly into
standard model states, showing that they are significantly restricted if the
new scalar states needed for UV completion are at the TeV scale. Alternatively,
if hyperbaryon number is conserved, the charged relic can decay into a neutral
hyperbaryon. Such theories are strongly constrained by direct detection, if the
neutral constituent hyperquark carries color or weak isospin, and by LHC
searches for leptoquarks if it is a color singlet. We show that the neutral
hyperbaryon can have the observed relic abundance if the confinement scale and
the hyperquark mass are above TeV scale, even in the absence of any hyperbaryon
asymmetry.
