  The origin of very low-mass hydrogen-burning stars, brown dwarfs, and
planetary-mass objects at the low-mass end of the initial mass function is not
yet fully understood. Gravitational fragmentation of circumstellar discs
provides a possible mechanism for the formation of such low-mass objects. The
kinematic and binary properties of very low-mass objects formed through disc
fragmentation at early times (< 10 Myr) were discussed in Li et al. (2015). In
this paper we extend the analysis by following the long-term evolution of
disc-fragmented systems, up to an age of 10 Gyr, covering the ages of the
stellar and substellar population in the Galactic field. We find that the
systems continue to decay, although the rates at which companions escape or
collide with each other are substantially lower than during the first 10 Myr,
and that dynamical evolution is limited beyond 1 Gyr. By t = 10 Gyr, about one
third of the host stars is single, and more than half have only one companion
left. Most of the other systems have two companions left that orbit their host
star in widely separated orbits. A small fraction of companions have formed
binaries that orbit the host star in a hierarchical triple configuration. The
majority of such double companion systems have internal orbits that are
retrograde with respect to their orbits around their host stars. Our
simulations allow a comparison between the predicted outcomes of
disc-fragmentation with the observed low-mass hydrogen-burning stars, brown
dwarfs, and planetary-mass objects in the Solar neighborhood. Imaging and
radial velocity surveys for faint binary companions among nearby stars are
necessary for verification or rejection for the formation mechanism proposed in
this paper.
