They probably wouldn't exist, but you might get away with one or two.
The problem lies in Mendeleev's table: all substances are defined by the number of protons Z in their nucleus, and we know what substances are created with N protons, with N between 1 and 115-ish. We also know that, roughly, beyond a certain point, the atom nucleus grows too big for the strong nuclear force to be able to keep it together.
So, beyond a certain Z, atoms are unstable; and with lower Zs, we know what we would get and it isn't any "star metal". In other words, your star metal has no "slot" where it could exist.
However, there seems to be an "island of stability" with substances that do not self-destruct almost instantly, but last some fractions of a second before disintegrating.
You might therefore posit a further island of stability, with Z beyond 130 (say), where unforeseen and not necessarily explained "geometric properties" allow one or two substances to be almost indefinitely stable. These substances would almost certainly be metals, incredibly dense - more than lead or uranium, possibly more than osmium; soft and malleable, decent electricity conductors.
The reason they only exist in outer space is that the energy required to create them is immense - even more than heavy metals. These "superheavy metals" require a hypernova explosion to be created in any significant quantity.
A relevant use of such metals is less clearly designed, though. You need something that only alien phlebotinum can do, something extremely valuable - enough to launch a thousand starships to mine it from remote, hostile places.
Perhaps some weird chemical property - who knows, a catalyzer with the ability of transferring phased electrical energy directly into precise, customised chemical bonds. This could become the easiest way of cleaning up a polluted Earth's atmosphere, precipitating carbon and nitrous/sulphur oxides (imagine a sieve through which enormous quantities of air flow freely - all the while silently shedding an impalpable black diamond, soot or fullerene powder that gets scrubbed).
Or they could have unexplained, incredible tensile strength (either alone or in combination with, say, carbon nanotubes). This would make them incredibly valuable for the construction of space elevators, which in turn allow cheap (think 100x or even 1000x) and environment-friendly space launches (this happens in Timothy Zahn's Spinneret).
Or they could be the essential component for Goldberg quantum resonators, devices capable of measuring and transferring precise, minute and controlled amounts of energy within a radius of a foot or so. Coupled with a powerful enough computer, these devices can, in a few hours or days depending on the volume treated, cure not only cancer but old age too (they would be a miniaturized version of Iain M. Banks' Culture's effectors, capable of manipulating matter at the atomic level through the fourth dimension). The length of a treatment (you need to rewrite trillions of cells in a body) would mean that the only practical way to process more people within their lifetimes would be to build more devices, but to do so you need space metal for the "recording heads". Even Earth rare metals do not allow the required precision, making the machines worth billions, their services auctioned to the highest bidder (something vaguely like this, minus the space metal, occurs in E. C. Tubb's S.T.A.R. Flight).
Other possibilites - does it need to be a metal? Or a "natural" occurrence?
Space iron cannot be different from Earth iron because iron is iron everywhere (this is the premise of "Omnilingual" by H. Beam Piper).
But composite materials can exist in a much greater variety of configurations, some of which might not exist on Earth. So, for example, the radiation spectrum of a faraway sun might transform ordinary cotton into some exotic material, too costly to reproduce otherwise (this is Isaac Asimov's The Currents of Space).
Or drugs. Lots of leeway there.