Hello and thank you for your question!
There is a hardship commission in (as far as I know) every federal state in Germany. Their composition, mode of operation and requirements slightly vary. Therefore, I recommend to check the specific information regarding the hardship commission in your federal state. In Berlin, for instance, the members of the hardship commission offer counselling hours for potential applicants - please see this paper for contanct details. In Bavaria (Bayern), I recommend to contact a member of the hardship commission directly as well (please see their details here). The Bavarian hardship commission i.e. usually requires (among other criteria) a minimum stay in Germany of 5 years and a good level of integration (proven throgh i.e. good level of German language, work, school/vocational training performance, voluntary work etc.) and urgent personal or humanitarian reasons to stay in Germany. It is important that applicants have exhausted all other possibilities of getting any kind of residence permit and are actually obliged to leave the country at the time of applying.
I hope this helps and please don't hesitate to share with us your approximate location if you need more specific information about "your" hardship commission.
All the best,
Meike