Is it permissible to purchase the right to reside in a compound built with an interest-based loan, given that there is no alternative for housing in this manner, and the purchase was made with unborrowed money?

If the intent of the question is regarding the ruling on your participation in the ownership of a property, or in purchasing a share in a property where some of those who bought or participated in it have paid the price through an interest-based loan; then your purchase of a share in this property is permissible, and the sin of engaging in an interest-based loan falls upon its perpetrator.