In this topic, I have given some planetary combination which represents the living in the rental house.

In Horoscope chart, 4th house represents the Mother, Vehicle, House, Land, Business, etc.. 6th house represents the disease, debt, enemies, money loss, etc.. 

The person, who have below planetary position in birth chart may live in rental house

1. The conjunction of 4th house lord and 6th house lord.

2. Aspects between 4th and 6th house lord.

In this, if 4th house lord becomes strong, then the person will have own house.