Parallax is appreciable only for nearby stars; even the nearest, Proxima Centauri, is displaced from its average position by less than an arcsecond as the Earth revolves in its orbit.
For stars with a known parallax, knowledge of the radial velocity allows the proper motion to be expressed as an actual space motion in 3 dimensions. The proper motion is, in fact, a snapshot of the transverse component of the space motion, and in the case of nearby stars will change with time due to perspective.
SLALIB does not provide facilities for handling parallax and radial-velocity on their own, but their contribution is allowed for in such routines as sla_PM, sla_MAP and sla_FK425. Catalogue mean places do not include the effects of parallax and are therefore barycentric; when pointing telescopes etc. it is usually most efficient to apply the slowly-changing parallax correction to the mean place of the target early on and to work with the geocentric mean place. This latter approach is implied in Figure 1.
SLALIB --- Positional Astronomy Library