From a shari’a perspective, it is permissible to leave a pledged asset/collateral, with respect to a credit transaction, in the possession of the debtor/pledgor though in principle, the pledged asset should be retained in the possession of the creditor/pledgee. It is also permissible that the pledged asset be kept with a trustworthy third party.

Al-rahn ghayr al-heyazi (الرهن غير الحيازي) is Arabic for non-possessory pledge  or security pledge /registered pledge.