In addition to any one-time payment that is necessary to get a house, characters must pay a monthly rent for their houses. Rents can vary greatly depending on the size, location and furnishing of a house. Since landlords are suspicious people the rent must always be paid in advance. The money is automatically debited from the character's bank account. If it does not contain enough money when the rent is due, the owner of the house will receive a warning letter in the inbox for one week (starting at the day on which the rent is due). If the rent is not paid during this week, the character will be evicted from the house and all belongings in the house will be moved into the inbox of the character. Note, however, that large pieces of furniture that do not fit in a backpack will stay in the house. Furthermore, all characters on the player's account are blocked from renting another house for 30 days. The house concerned will be ready to be auctioned again.
I also wanted to add I had a friend get kicked out of his house due to not paying rent as well and he didn't have to pay the rent after he got kicked out. The only penalty listed seems to be that the player's account is blocked from renting a house for 30 days!