It has commonly been assumed that accretion onto a magnetosphere is inhibited at low accretion rates, due to the centrifugal barrier presented by the star (the so-called 'propeller' regime). However, recent work has demonstrated that at low accretion rates a large amount of mass can remain confined in the disc, creating a 'dead disc' that extracts angular momentum from the star without accreting or ejecting a significant amount of mass. These 'dead discs' often become unstable, initiating cycles of accretion onto the central object. I will present the main predictions of this model, and demonstrate how it may be relevant for stars with strong magnetic fields accreting from discs. In neutron stars, it may explain the peculiar 1Hz quasi-periodic oscillations seen in the accreting millisecond X-ray pulsars SAX J1808.8-3658 and NGC 6440 X-2 as well as low-mass X-ray binaries like Cen X-4 that show accretion even during quiescence.