The aim of the bill is to create legal certainty for all UK nationals and their families who have made use of the EU freedom of movement and made decisions affecting their lives in Germany in the legitimate expectation that this freedom of movement would continue.
The bill ensures that all UK nationals and their families residing in Germany under EU freedom of movement rules at the time of withdrawal will be able to receive a residence permit. Furthermore, the bill creates the necessary conditions under residence law for these persons to continue to have access to the German labour market.
The law must still be approved by the German Bundestag. It will only enter into force in case of a withdrawal without the Withdrawal Agreement.
In addition to the bill, the German Government intends, by ordinance, to temporarily exempt those affected from the requirement to hold a residence permit in Germany. The aim is to give both those affected and the foreigners authorities sufficient time to apply for and issue the necessary residence permits.
You can find the text of the bill here (in German).