Welcome back to the Wefugees Community and thank you for reaching out to us again.
Without knowing the background of the family, I was thinking that she might qualify for a residence permit according to section 25a of the German Residence Act "well integrated juvenile".
I paste the law here:
Granting residence in the case of well-integrated juveniles and young adults
(1) As a general rule, a juvenile aged 14 to 18 or a young adult aged 18 - 21 whose deportation has been suspended is to be granted a temporary residence permit if
1. the foreigner has resided in the federal territory for four years without interruption either by virtue of holding a temporary residence or permanent settlement permit, by virtue of his or her deportation having been suspended or by holding permission to remain pending the asylum decision,
2. the foreigner has successfully attended school in the federal territory for, as a rule, four years or has acquired a recognised vocational or school-leaving qualification,
3. the application for the temporary residence permit is filed before the foreigner reaches the age of 21,
4. it appears, on the basis of the foreigner’s education and way of life to date, that the foreigner will be able to integrate into the way of life in the Federal Republic of Germany and
5. there is no concrete evidence to suggest that the foreigner is not committed to the free democratic basic order of the Federal Republic of Germany.
For as long as the foreigner attends school, vocational training or higher education, claiming public benefits for the purpose of ensuring his or her subsistence does not preclude the granting of the temporary residence permit. A temporary residence permit is to be denied if deportation has been suspended on the basis of false information furnished by the foreigner or on the grounds of deception by the foreigner as to his or her identity or nationality.
(2) The parents or parent having the right of care and custody of a foreign minor who holds a temporary residence permit in accordance with subsection (1) may be granted a temporary residence permit if
1. deportation has not been prevented or delayed on the grounds of false information or deceit with regard to identity or nationality or due to a failure to meet reasonable demands to eliminate obstacles to departure and
2. subsistence is ensured independently by means of an economic activity.
The minor children of a foreigner who holds a temporary residence permit pursuant to sentence 1 may be granted temporary residence permits if they live with the foreigner as a family unit. As a general rule, a spouse or civil partner who is living with the beneficiary referred to in subsection (1) as a family unit is to be granted a temporary residence permit if the conditions of sentence 1 are met. Section 31 applies accordingly. As a general rule, a minor, unmarried child who is living with the beneficiary referred to in subsection (1) as a family unit is to be granted a temporary residence permit.
(3) No temporary residence permit pursuant to subsection (2) may be granted if the foreigner has been convicted of an offence intentionally committed in the federal territory; fines totalling up to 50 daily rates or up to 90 daily rates in the case of offences which, pursuant to this Act or the Asylum Act, can only be committed by foreigners, are ignored as a general principle.
(4) The temporary residence permit may be granted in derogation from section 10 (3) sentence 2
As the family took their case even to a higher court, I assume they have a lawyer, right? Maybe they can discuss this type of residence permit with the lawyer and ask for his/her opinion.
However, also don't hesitate to get back to us if you need some further explanations on the requirements or if you have any other questions.
All the best,