And keep in mind before your read this that half of those rejected asylum seekers actually selected for deportation are, well, never actually deported (they just don’t bother to show up for the flight, for instance).

If an application for asylum is rejected, the Federal Office for Migration and Refugees issues a refusal notice and a deportation notice. The refusal notice says you have to leave within a certain time and warns that police will deport you if you don’t comply.
However, everyone has the right to appeal the refusal and postpone the deportation. There are several opportunities to appeal in the courts. The first appeal is through the administrative court. If this fails, you can take the case to a higher administrative court, and then in rare cases, to the Federal Administrative Court. After this, you can submit a complaint to the Federal Constitutional Court. If you believe that a deportation decision is violating your human rights, it is possible to appeal to the European Court of Human Rights in Strasbourg.
Even if you do not appeal a rejection, deportation can only take place if it is “practically possible and compatible with the law.” If deportation is not possible due to legal or medical reasons, the Migration Office can grant a tolerated residence permit. Currently, nearly 200,000 people in Germany hold a tolerated stay. Almost half of them have been tolerated for at least ten years.
Fast jede zweite geplante Abschiebung abgebrochen.