Do they lock unowned houses

There is no such thing as an unowned house. The builder who built it owns it first, then they sell it to an owner, who sells it to another owner, and so on. If it is foreclosed on, the bank owns it. If it left vacant after the owner moves away, that owner continues to own it. If the owner dies and no on inherits the property, the state owns it.

Vacant houses are generally kept locked.