The proverb, ‘A rolling stone gathers no moss’ means: 'People who are always moving, with no roots in one place or another, avoid responsibilities. However, this has its own disadvantages such as not being able to create their own niche/ build relationships in a single place'. Hence, the phrase, ‘gathers no moss’ as given in option C completes the proverb.
The other words given in options A, B and D do not complete the proverb. Hence, these options are incorrect.