I am sorry to hear about your Ausbildung. Firstly, it is important to know that you have to tell the Ausländerbehörde about this within two weeks of being notified about the termination. This is in paragraph 82 of the Residency Act:
It is possible to get a new permit for the purpose of looking for a new Ausbildung for up to 6 months. This is possible in cases where the termination was not due to the foreigner’s own actions. A clear case here would be if a person was doing an Ausbildung with a company that shut down and they lost their Ausbildung place as a result.
The law does not, however, detail which reasons for a termination are to be seen as due to the foreigner’s own actions. The Ausländerbehörde will expect you to provide an account of why the termination happened and will then decide whether you are entitled to a 6-month permit to **** for a new place. I recommend you try to get help if making a written statement to the Ausländerbehörde. If you need to know where to go, you can let us know what part of Germany you are in. There are also often organisations which specifically help migrants to find an Ausbildung. If you do not know of any, we can try to find one near you.
Here is some additional information about the Ausbildung permit (links translated with an online translation tool):