Thank you for getting back to me so quickly.
I think I understand what you are asking now - you have been rejected twice in Germany and are wondering what your options are to stay in Europe, is that correct?
First of all: Here is some really important information about your Duldung status and your options from the Flüchtlingsrat Leverkusen: http://www.fluechtlingsrat-leverkusen.de/eng/3.4.5_duldungen.htm
As it says on the website,
"Duldung means that
- the allocation to a community persists,
- the limitation of freedom of movement persists and can even be intensified,
- a residence permit for family members is excluded, and
- a work ban can be placed.
An obligation to leave Germany arises if the reasons for escape in the asylum request were rejected and the rejection is legally binding.
Note: If you receive a notification on the legally binding rejection of your asylum application you should immediately inform the alien’s office in writing that you are willing to return voluntarily."
Regarding your second question: If you are asking whether or not you are able to claim asylum in a different EU-country (is that what you mean by "When is my Dublin case supposed to expire"?): You won't be able to claim asylum in any other EU-country after claiming asylum in Germany, even if it was rejected, due to the Dublin III Regulations.
There is, however, a way to avoid Dublin III. If you leave the EU for more than three months, your case can be viewed as "reset" - which means applying for asylum again in a different EU-country becomes possible. Please read more about it in Marcel's answer on the following thread:
Claim asylum for second time in EU
Also, you can have a look at this explanation of Dublin III by openmigration: https://openmigration.org/en/analyses/what-is-the-dublin-regulation/
Have you reached out to any legal advice centers/ lawyers yet? I would highly recommend it, as they are able to have a closer look at your case and give you a more detailed answer on the options you have.
Do feel free to reach out to us again if you need any further assistance!