The Abandoned House in Markarth is a seemingly uninhabited and empty home which the Vigilants of Stendarr believe is being used for Daedra worship. Vigilant Tyranus will be asking passers-by for their assistance in investigating the house.
After completion of the first part of "The House of Horrors," the house can be used as a free alternative home without ever completing the quest (leaving it open, or failing it intentionally). However, the Dragonborn cannot have a spouse live in this house, as it is technically unowned.
There are numerous safe containers (62 in total), an unowned bed that confers the Rested bonus, as well as services available close by at the entrance to Markarth. The containers inside the house are safe for permanent storage. On the bottom floor a cave can be found, leading to a shrine of Molag Bal. However, it does not contain alchemy, cooking or enchanting facilities.
On the outside of the house, there is a Shadowmark that indicates that the house is empty.
Molag Bal has asked the Dragonborn to cleanse his altar in the abandoned house in Markarth by luring a priest of Boethiah to him.