  (abridged) We describe the discovery of an extremely wide pair of low-mass
stars with a common large proper motion and discuss their possible membership
in a Galactic halo stream crossing the Solar neighbourhood. (...) The late-type
(M7) dwarf SSSPM J2003$-$4433 and the ultracool subdwarf SSSPM J1930$-$4311
(sdM7) sharing the same very large proper motion of about 860 mas/yr were found
in the same sky region with an angular separation of about 6\degr. From the
comparison with other high proper motion catalogues we have estimated the
probability of a chance alignment of the two new large proper motions to be
less than 0.3%. From the individually estimated spectroscopic distances of
about $38^{+10}_{-7}$ pc and $72^{+21}_{-16}$ pc, respectively for the M7 dwarf
and the sdM7 subdwarf, and in view of the accurate agreement in their large
proper motions we assume a common distance of about 50 pc and a projected
physical separation of about 5 pc. The mean heliocentric space velocity of the
pair $(U,V,W)=(-232, -170, +74)$ km/s, based on the correctness of the
preliminary radial velocity measurement for only one of the components and on
the assumption of a common distance and velocity vector, is typical of the
Galactic halo population. The large separation and the different metallicities
of dwarfs and subdwarfs make a common formation scenario as a wide binary
(later disrupted) improbable, although there remains some uncertainty in the
spectroscopic classification scheme of ultracool dwarfs/subdwarfs so that a
dissolved binary origin cannot be fully ruled out yet. It seems more likely
that this wide pair is part of an old halo stream. (...)
