Thank you for your question and sorry you had to wait so long for an answer!
If you don't have a valid visa and cannot enter the German territory, you can apply for asylum in the transit area of following airports: Berlin-Schönefeld, Düsseldorf, Frankfurt/Main, Hamburg and Munich. You will have to stay in the transit area until a decision is made on wether your case will be processed on the German territory or you are returned to your country of origin or the country you flew from. The process can take 2 to 19 days, depending on if you have to appeal the decision or not. This is a special, fast procedure. I recommend you to gather as much evidence as you can on the grounds that lead you to leave your country and why you cannot return. You can (and should!) ask for legal support at the airport.
Here is more information on the procedure.
I hope this still helps. Don't hesitate to a add a comment if you need additional information!
All the best,