(This article is a collection of info received from human rights lawyers)
The MFSA (regulatory authority in Malta) is starting to pressurize the 5 main banks in Malta that are obliged to open basic payment accounts (APS, BNF, BOV, HSBC and Lombard). They are basic accounts into which one can receive their salary and make payments Any licensed bank in Malta with at least 5 branches is obliged to open basic payment accounts to any person resident within the European Union (meaning Malta or any of the other 27 Member States). This also applies to MT residents in other EU states.
One can check the Payments Directive to see that the right to a basic bank account is applicable also to asylum-seekers, persons with rejected status and people with no permanent address or homeless. This right derives from the EU Payments Directive and MFSA was obliged to ensure its application as local banks were ignoring its implementation.
A valid identity document for basic payment accounts purposes includes other than any Passport or ID card, the Asylum Seekers Certificate, THP document, Protection Card issued by RefCom, Identification Document for individuals that cannot be repatriated. On the FIAU, website, it is possible to have detailed visual information showing the documents that should be accepted by banks. (detailed info here: FIAU (PDF)
However, AML laws say that the individual must be identified and such identity verified, therefore, it is arguably possible for a migrant with no ID/passport to open such account as long as it is identifiable (a number of personal data are provided) and such information is verified by documents issued by third independent parties.