In Bangladesh, we use the word "গৃহপালিত" for an opposition party that was installed by a ruling regime through a rigged election. The main duty of this party is to give the vibe that the country is democratic. They do nothing that may harm the ruling party in anyway. So, what is the correct phrase in English for such an opposition party?
The word "গৃহপালিত" literally translates to pet, domestic, or domesticated. I have seen some of our English daily using the term domesticated for such a party. For example, here. But I think there might be a better phrase that non native English speakers like me are not aware of.