If by "outlive" you mean "continue to exist"... the Voyagers have a finite useful lifespan defined by the output of their RTGs, and that's expected to drop below useable levels sometime around 2025 (for both craft). But they'll still be out there, barring a random encounter with an asteroid or something.
I think that two grains of sand on beaches of the opposite ends of the Earth are probably more likely to interact than a random rock and a tiny satellite that has left the Solar System into interstellar space.
In fact, in about 40,000 years, Voyager 1 will pass within about 1.6 light-years of the star Gliese 445. It's also likely that it's as close to a star as Voyager 1 will be again, ever.
Space is pretty empty compared to Earth or even our own Solar System.
I know this sounds contrived, but imagine the mission beeing not reliant on continous operation, but just a operation of any kind to continue.
Could one just harvest the background radiation for energy, and switch on, once some storage capacitator reaches a critical threshold. A device harvesting this weak, but continous energy source, could work indefinatly?
