The owner of a foreclosured property can not rent it. With judgement n. 13216/2016, june 27, 2016, the Italian Corte di Cassazione stated that the tenant can continue living in the house, because only the keeper (custode) or the enforcement court may remove him. 

Moreover, only the keeper or the the enforcement court can authorize the lease contract (art. 560 codice di procedura civile): management of  foreclosed property belongs only to the caretaker.

Here, the judgement: “Although leasing a foreclosured property, without the permission of the judge, not undermine the validity of the contract but only its unenforceability to the creditors and the assignee, the contract thus concluded does not affect the lessor-owner, but the landlord-caretaker, and the management is up to the caretaker”.