Isolated magnetic neutron stars are considered at the end of the phase of coherent pulsar emission when accretion from the interstellar medium becomes important but rotation affects the inflow dynamics. When the centrifugal acceleration at the Alfven radius exceeds the gravitational one, a process of piling up of matter is expected to take place, yielding the compression of the magnetospheric boundary. Prompt matter infall to the neutron star surface occurs when the gravitational energy density has increased with time to overcome the centrifugal barrier. Recurrence times are estimated, and it is suggested that aging neutron star can undergo accretion with intermittent or quasi-cycling behavior when passing from the isolated radio pulsar phase to quiescent steady accretion over the life time of the Galaxy. An analogous process of build up of the magnetodipole energy is envisaged and it is proposed that a relativistic jet may form. Although on energetic scales much more modest, the picture has some resemblance with the cauldron model of SS 433 (Begelman & Rees 1984). The consequences on the detectability of old isolated neutron stars are shortly discussed.