During the low-speed chase, the First Order chases the Rebel fleet until its ships run out of fuel. When they do run out of fuel, the First Order ships are able to overtake them and destroy them.
This makes absolutely no sense, as the laws of physics dictate that an object's inertial movement will keep it moving at the same rate absent any external force. The chase is taking place in the vacuum of space, so even if the ships do run out of fuel, they'll continue to move at the same speed they did when their thrusters were functioning properly. There's no friction in space, so until the ships get caught in some massive object's (such as a planet's or star's) gravitational field, they would continue to move at the same speed, potentially for years, decades, centuries, or even millennia.