I am sorry to hear about your situation and I hope you are doing well.
Is your question directed to the transmission period (Überstellungsfrist) of 6 months? I think this deadline is not something you can just outlive.
The transfer shall be made within six months from the date of consent of Estonia. If the person concerned is in custody, the transfer period is 12 months. If the person concerned is a fugitive, the transfer period is 18 months. (2019, BAMF)
Dear @meike and @mbeon-éanna, could you perhaps give an tip on the Dublin transfers (Dublinverfahren and transfer deadlines( Überstellungsfrist)? I have found a link here
https://***.proasyl.de/hintergrund/praxishinweise-zur-aktuellen-aussetzung-von-dublin-ueberstellungen-und-ueberstellungsfristen/ that may be helpful, but since I am not an expert, I did not find it easy to summarize the information in a helpful way.
With my answer I hold together the general problem, with which many persons living in Germany are confronted, it will perhaps not be new to you.
An illegal stay in Germany without a visa, a Duldung or Aufenthaltsgestattung is punishable by a fine or Prison of up to one year (see § 95 AufenthG).
Every person has the right to the "highest attainable standard of physical and mental health".This is stated in the UN Social Covenant of 1966 (Art. 12).
Nevertheless, many people living illegally in Germany find it difficult to exercise their rights to housing, education, health care and other social benefits. This is because they are often asked for their residence title and public authorities are obliged to inform the Aliens' Registration Office, Ausländerbehörde (obligation to transmit Meldepflicht).
In medical emergencies, doctors are excluded from this obligation.
People without residence status are generally entitled to treatment for acute illnesses and pain conditions. However, for further treatment they often need a treatment certificate from the social welfare office, which must report.
It is best for people without papers to turn to non-governmental institutions such as Malteser Migranten Medizin, Medinetze or clearinghouses. (2021, Rüffer Anita)
Getting an apartment is also difficult. Once an apartment is found, it must be registered with the local residents' registration office. "A social apartment can only be obtained with a certificate (Wohnberechtigungsschein). For this, personal data must be disclosed.
In a refugee shelter, the identity would also have to be disclosed.(2021, Rüffer Anita)
I hope we can gather more information to help you and our community.
With warmest regards
2019: BAMF. Prüfung des Dublin-Verfahrens
2021: Rüffer Anita: Rechte von Menschen ohne Aufenthaltserlaubnis, online unter: https://***.caritas.de/hilfeundberatung/ratgeber/migration/lebenindeutschland/rechte-von-menschen-ohne-aufenthaltserla (letzter Zugriff: 10.10.22)