Wife overstayed her visa unintentionally, need advice

Hi all,

I'm an MBA student living in Bremen. I already have my residency permit until 2020, but we didn't apply for Family Reunion Visa yet because I don't have sufficient accommodation for my wife and daughter.

This is why they decided to visit me on a Schengen Visa as tourists. However, they didn't realize that even though the duration between the beginning and end of the visa was 33 days, it was stated in the visa sticker that the duration of stay was only 20 days.

So when they were going through passport control when going back, they were detained by the border police and were issued a case for this. They were eventually let go by the kind German police in order to catch their plane but they were told that a fine would arrive by letter to their home address.

What worries me is that it's been 3 months now and they still didn't receive this fine. I'm worried this might cause further issues along the road when we actually apply for the family reunion visa.

Is there any place where I can check for this fine in Germany? How much would the fine for overstaying 12 days? Would she get a ban from entering again? Any help/advice on these regards would be greatly appreciated.