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 a factor ∼10 above 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 metastable 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.