If somebody does not trade and just deposits, then wants his fund back in the same format he sent them, then there is no need for ID verification.

The main anti-money laundering duties (enshrined in Italian law)  relate to:

Customer due diligence
Data retention duties
and
Reporting duties.

At this regard, the obliged entity shall:

carry out an adequate client and/or beneficial owner due diligence in case of ongoing business relationship or occasional transaction involving the transfer or the handling of payment of an amount equal to or higher than 15,000 Euro or in any case, i) in case of doubts concerning the truthfulness of the data obtained or suspects of money-laundering or terrorism financing regardless of any exemption applicable; ii) clients located in high risk countries identified by the European Commission; iii) cross-border correspondence with a corresponding credit institution or financial institution in a third country; iv) ongoing professional relationships or transaction performance with clients and in case of politically exposed persons.

shall retain a copy of the documents collected during the customer's due diligence, indicating: i) the relevant date of the establishment of the business relationship; ii) personal data of the customer and/or the beneficial owner iii) the scope and nature of the legal relationship or of the transaction in place; iv) means of payment used by the customer.

shall submit without delay a suspicious transaction report to the UIF (Financial Intelligence Unit for Italy) when they become aware of, suspect or have reasonable grounds to suspect that terrorism financing or money laundering are in process or terrorism operations are being carried out or attempted, or whatever funds, regardless of their size, come from criminal activity.