the law does not allow you to have a duldung while the Ausbildung takes place but after succefully comletion of the Ausbildung you might be granted a Aufenthaltserlaubnis in order to get a job.
§ 60a Abs. 2 S. 4 ff. AufenthG:
During such this type of training programme, you will receive a tolerated residence permit or so-called "Duldung" for the duration of your training. If you stay in the company or institute after completing your training there or manage to find another job immediately, you will be issued a residence permit, valid for 2 years. If not, you will have 6 months time to search and find a new job in Germany.
Important: In principle, you are entitled to vocational training toleration or "Ausbildungsduldung".
Legally you are not allowed to be deported while being in your Ausbildung.
In order to obtain the "Ausbildungsduldung" you either need a Passport from your home country or a substitute (Passersatz).
Whether they might use your Identity Documents to deport is something that cannot be answered by me but should be discussed with your lawyer, as he/she knows the case best and the people in charge of your case at the Ausländerhörde.
I hope we could assist you, if you have further question please do not hesitate to contact us in the community.