In Kerbal Space Program, a space exploration game made with Unity, Floating origin technique is used to overcome the floating point precision issues. While in map view, the world (a scaled space with miniature celestial bodies) is recentered around the camera every frame so glitches don't occur when viewing unsafely distant planets. But when such planets are observed from an 'unsafe distance' (more than 10 000 units in scaled space), they're still rendered normally. Why don't floating point issues occur?
I'm fairly sure floating point rounding errors don't mean that an object will be absolutely rendered incorrectly when far away.
It just means that the probability of the sun being exactly where it is supposed to be is smaller the farther away from the origin it is.
However, you might not be able to notice if the sun is at the wrong place with an error of 10 km for instance. Since the sun jumping between 10 km is hardly noticeable from earth. It wouldn't even move a single pixel.
You also have to take into account that Kerbal uses many cameras to render a single scene. Three, if I remember correctly. One for the cockpit or ship, one for the landscape, and one for celestial objects. These cameras have individual near/far rendering planes.
I hope this answers your question.
This video goes into greater detail: https://youtu.be/mXTxQko-JH0?t=399