When they come within one light year of one another, they will emit gravitational waves that will radiate further orbital energy until they merge completely.
Partly for this reason, it is still the unit preferred in astronomy and astrophysics, though the light year remains prominent in popular science texts and more everyday usage.
This was coherent with the estimation made by astronomers in 1938, but after some additional measurement, this distance was re-estimated at 14.3 light year.