This is something I do from time to time. If you look at the music in the link below, you can see that bar #1 has two notes, then a rest.
The normal way to play this would be to stop the bow motion at the rest. This is fine, but there’s another way to bow this, so that the rhythm remains the same as if you played and sounded all of the 8-note phrase of bar #2.
You could play with ‘ghost’ bowing, which in this case would be simply D-U-D-U. On the rest, (note #3) you play a down bow, but using zero bow pressure on the string. Same with the next rest (‘note’ #5).
The main purpose of this bowing is simply to preserve the rhythm of D-U-D-U. It’s more of a rhythmic device than anything else.