Problems when exiting Schengen area on expired residence permit

Question

My girlfriend is a Mexican passport holder.

She studied in Netherlands for her masters and she possesses a residence card/permit from The Netherlands (the expiry date on the card says 1st Dec. 2016).

She is living with me at the moment in Berlin and already has her tickets to fly back to Mexico on 30th Nov. 2016 (1 day before the "expiry date" on her Dutch residence card).

She received an email yesterday (2nd Nov. 2016) from her University in Netherlands that because she's not a student at the University anymore, her status has been informed to the IND (Immigration and Naturalization service of Netherlands) and that her residence card is invalid from 1st Sept. 2016 (we both graduated in Aug./Sep. 2016) doesn't matter what "expiry date" is mentioned on her residence card. So technically she's been living illegally since past two months in Berlin with me!

My question is: would there be an issue when she'll go through border/passport control in Berlin (on 30th Nov. 2016)?

I understand that Mexican nationals enjoy 90 days in 6 months tourist stay in Schengen but this period doesn't automatically start after your long-term residence permit or visa expires. So is it necessary that she leaves Schengen area (to lets say UK) and enter again as a tourist before her flight out of Berlin.

Edit 1: Fast forward to 30th Nov. 2016 Girlfriend was able to exit Germany without any hassle. The passport control officer put an exit stamp on her passport but then the flight was cancelled. She stayed one more night in a hotel and finally took off from Köln on 1st Dec. 2016 at 23.30 (30 minutes before the expiry of her RP). Also learned that passport control is flexible in these matters. They told her that they'd have let her fly if the flight was cancelled again for next day (when her RP would have been "visually" invalid.)

Answer 1

I understand that Mexican nationals enjoy 90 days in 6 months tourist stay in Schengen but this period doesn't automatically start after your long-term residence permit or visa expires

You are incorrect, there's no need to reenter the Schengen area after the expiration of one's national visa. According to the Schengen Border Code:

Periods of stay authorised under a residence permit or a long-stay visa shall not be taken into account in the calculation of the duration of stay on the territory of the Member States.

So your girlfriend's status as a citizen of an Annex II country would trigger immediately after her residency permit expires. She is therefore free to stay in the Schengen area for 90 days after September 1st.

My question is: Would there be an issue when she'll go through border/passport control in Berlin (on 30th Nov. 2016)?

No, there won't be a problem at the border crossing. Just make sure that your girlfriend presents her residency permit to verify her former status as a long-term resident.