The outcome of the flight of an imaginary Arrow is unknowable.
However, if an arrow were launched into space, the arrow would not travel through a void. It would encounter particles and dust. These would act on the arrow. Over time it would scour and pit the surface and erode it away, wood first, later metal. It might erode, with time, into its consitutant atoms.
Gravity, as far as we know, acts on all things. At some point it would act to capture the arrow—if it had not yet been scoured to particles— and pull it toward a galaxy, a sun, a planet. It might become a satellite around a Sun. It might land on a planet and become part of its mass, it might dissipate and become part of a dust cloud....
Oops! Duplicate post. Sorry, I was caught in a time loop! (ButI managed to escape!)