Until summer 2016, work permits were granted to people in asylum procedure and the ones with a “Duldung” only if no German or EU citizen had applied for the position ("Vorrangprüfung"). Currently, this regulation has been suspended until August 2019 in almost all federal states of Germany. The priority test ("Vorrangprüfung") is still valid in some regions of Bavaria (e.g. Munich, Augsburg, Nürnberg), in parts of North-Rhine Westphalia (e.g. Dortmund, Bochum, Essen) and in Mecklenburg-Vorpommern. However, it applies only during the first 15 months of your stay. Afterwards, only the general terms of your contract will be checked but there will be no priority tests.
The priority test is no longer required if you start vocational training or an internship or in case you practice a highly specialised job.