Dear @Sidra,
Welcome back to the Wefugees Community and thank you for reaching out to us.
I assume your friend holds a residence permit according to §28 of the German Residence Act as mother of a German child (not as spouse of a German citizen as they are not married), right? As family member of a German, people may be enitled to receive the permanent residence (Niederlassungserlabnis) already after three years (instead of at least 5 y.) if they fulfill all the requirements.
One of the conditions is the secured livelihood of the family (could be secured by income of any member of that family). As neither your friend nor her partner are working, the are dependent on social money, most probably from the Jobcenter. As long as they are dependent on social money (the Kindergeld is not harming an application though), your friend will most likely not be able to get the permanent residence permit. Please see the full list of requirements here (on this page it is referring to procedures in Berlin - however conditions are similar in other regions/cities as well). On this website it also states that a German language level similar to B1 is required. This can be proven by a certficate (i.e. integration course) or may be demonstrated alternatively as well in the application process.
I hope this helps and please don't hesitate to get back to us if clarification is needed or if there are any further questions.
All the best,
Meike