For thermonuclear flashes to occur on neutron-star surfaces, fuel must have been accreted from a donor star. However, sometimes flashes are seen from transient binary systems when they are thought to be in their quiescent phase, during which no accretion, or relatively little, is expected to occur. We investigate the accretion luminosity during several such flashes, including the first-ever and brightest detected flash from Cen X-4 in 1969. We infer from observations and theory that immediately prior to these flashes the accretion rate must have been between about 0.001 and 0.01 times the equivalent of the Eddington limit, which is roughly 2 orders of magnitude less than the peak accretion rates seen in these transients during an X-ray outburst and 3-4 orders of magnitude more than the lowest measured values in quiescence. Furthermore, three such flashes, including the one from Cen X-4, occurred within 2 to 7 days followed by an X-ray outburst. A long-term episode of enhanced, but low-level, accretion is predicted near the end of the quiescent phase by the disk-instability model, and may thus have provided the right conditions for these flashes to occur. We discuss the possibility of whether these flashes acted as triggers of the outbursts, signifying a dramatic increase in the accretion rate. Although it is difficult to rule out, we find it unlikely that the irradiance by these flashes is sufficient to change the state of the accretion disk in such a dramatic way.
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