  For a quantum error correcting code to be used in practice, it needs to be
equipped with an efficient decoding algorithm, which identifies corrections
given the observed syndrome of errors.Hypergraph product codes are a promising
family of constant-rate quantum LDPC codes that have a linear-time decoding
algorithm called Small-Set-Flip ($\texttt{SSF}$) (Leverrier, Tillich, Z\'emor
FOCS 2015). The algorithm proceeds by iteratively applying small corrections
which reduce the syndrome weight. Together, these small corrections can
provably correct large errors for sufficiently large codes with sufficiently
large (but constant) stabilizer weight. However, this guarantee does not hold
for small codes with low stabilizer weight. In this case, $\texttt{SSF}$ can
terminate with stopping failures, meaning it encounters an error for which it
is unable to identify a small correction. We find that the structure of errors
that cause stopping failures have a simple form for sufficiently small qubit
failure rates. We propose a new decoding algorithm called the
Projection-Along-a-Line ($\texttt{PAL}$) decoder to supplement $\texttt{SSF}$
after stopping failures. Using $\texttt{SSF}+\texttt{PAL}$ as a combined
decoder, we find an order-of-magnitude improvement in the logical error rate.
