  Pair-instability and pulsational pair-instability supernovae (PPISN) have not
been unambiguously observed so far. They are, however, promising candidates for
the progenitors of the heaviest binary black hole (BBH) mergers detected. If
these BBHs are the product of binary evolution, then PPISNe could occur in very
close binaries. Motivated by this, we discuss the implications of a PPISN
happening with a close binary companion, and what impact these events have on
the formation of merging BBHs through binary evolution. For this, we have
computed a set of models of metal-poor ($Z_\odot/10$) single helium stars using
the \texttt{MESA} software instrument. For PPISN progenitors with pre-pulse
masses $>50M_\odot$ we find that, after a pulse, heat deposited throughout the
layers of the star that remain bound cause it to expand to more than
$100R_\odot$ for periods of $10^2-10^4\;$~yrs depending on the mass of the
progenitor. This results in long-lived phases of Roche-lobe overflow or even
common-envelope events if there is a close binary companion, leading to
additional electromagnetic transients associated to PPISN eruptions. If we
ignore the effect of these interactions, we find that mass loss from PPISNe
reduces the final black hole spin by $\sim 30\%$, induces eccentricities below
the threshold of detectability of the LISA observatory, and can produce a
double-peaked distribution of measured chirp masses in BBH mergers observed by
ground-based detectors.
