  A binary neutron star (BNS) merger can lead to various outcomes, from
indefinitely stable neutron stars, through supramassive (SMNS) or hypermassive
(HMNS) neutron stars supported only temporarily against gravity, to black holes
formed promptly after the merger. Up-to-date constraints on the BNS total mass
and the neutron star equation of state suggest that a long-lived SMNS may form
in $\sim 0.45-0.9$ of BNS mergers. We find that a SMNS typically needs to lose
$\sim 3-6\times 10^{52}$ erg of it's rotational energy before it collapses, on
a fraction of the spin-down timescale. A SMNS formation imprints on the
electromagnetic counterparts to the BNS merger. However, a comparison with
observations reveals tensions. First, the distribution of collapse times is too
wide and that of released energies too narrow (and the energy itself too large)
to explain the observed distributions of internal X-ray plateaus, invoked as
evidence for SMNS-powered energy injection. Secondly, the immense energy
injection into the blastwave should lead to extremely bright radio transients
which previous studies found to be inconsistent with deep radio observations of
short gamma-ray bursts. Furthermore, we show that upcoming all-sky radio
surveys will enable to constrain the distribution of extracted energies,
independently of a GRB jet formation. Our results can be self-consistently
understood, provided that BNS merger remnants collapse shortly after their
formation (even if their masses are low enough to allow for SMNS formation). We
briefly outline how this collapse may be achieved. Future simulations will be
needed to test this hypothesis.
