thank you for your question.
It depends usually the authorities will ask them to get a passport, in order to issue the Residence Permit.
If they cannot get a passport from the authorities of their home country, they have to proof that in written.
Who is entitled to a "Grey Passport":
Not olny people recognised as asylum seekers and refugees, but also those under subsidiary protection or a national deportation ban and other non-German citizens are entitled to a travel document to substitute their passport. However, this is only in the case an individual does not have any other passport and has no other reasonable way to apply for one. Legal rules and regulations regarding this situation are specified in the residence ordinance § 4 to 11. Since the passport issued in such cases is grey, it is also known as a "Grey Passport".
A travel document can also be issued to you if you are stateless, but there is always a case-by-case decision procedure. That is why the Grey Passport is officially called Travel Document for Foreigners and Stateless Persons („Reiseausweis für Ausländer und Staatenlose”).
The Grey passport might be an option but the requirements are quite rigid, therefore if the reason of their refuge is not a political and they have the chance to receive a residence permit I suggest to organize the passport from their home country.
I hope I could help you, please if further clearification is needed, do not hesitate to contact the community.