[cygx]

Objects don't outright disappear: As with other event horizons, they freeze in time and become redshifted as they approach the cosmological one (they also become fainter due to an increase in proper distance).

The cosmological event horizon is the light cone at future infinity and the asymptotic boundary of the observable universe: Light emitted within the horizon will take a finite time to reach us, whereas light emitted right at the horizon would take an infinte amount of time to arrive; in a way, light emitted beyond the horizon still moves towards us in the sense that the comoving distance decreases, but we'd have to wait a longer-than-infinte amount of time for it to arrive...