  The Be/X-ray transients V0332+53 and 4U 0115+63 exhibited giant, type-II
outbursts in 2015. Here we present Swift/XRT follow-up observations at the end
of those outbursts. Surprisingly, the sources did not decay back to their known
quiescent levels but stalled at a (slowly decaying) meta-stable state with
luminosities ~10 times that observed in quiescence. The spectra in these states
are considerably softer than the outburst spectra and appear to soften in time
when the luminosity decreases. The physical mechanism behind these meta-stable
states is unclear and they could be due to low-level accretion (either directly
onto the neutron stars or onto their magnetospheres) or due to cooling of the
accretion-heated neutron star crusts. Based on the spectra, the slowly
decreasing luminosities, and the spectral softening, we favour the crust
cooling hypothesis but we cannot exclude the accretion scenarios. On top of
this meta-stable state, weak accretion events were observed that occurred at
periastron passage and may thus be related to regular type-I outbursts.
