I applied for a German residence permit. The permit has been approved but I can only collect it after my visa expires. Is it illegal for me to stay In German between the time my visa expired and my permit collection appointment date?
According to § 81 Abs. 4 S. 3 AufenthG the residence is still allowed even after expiration of the visa, if one has applied for issuing a residence permit. Since you are already one step further (the permit has been approved), I personally do not see any reason for being worried there.
One could also ask for a paper confirming that application/approval has been made already. If one needs to travel, one could require Ausländerbehörde to issue Fiktionsbescheinigung according to § 81 Abs. 5.
The reason is probably not that you must wait until the visa expires, but must wait until the residence permit card has been produced. Only then can you collect it.
I assume you have a letter from the immigration office informing you that the residence permit has been approved and when the card, that is produced in the Federal Printing Office (Bundesdruckerei) in Berlin, is expected to be ready to be picked up.
This letter is proof of your legal status as a resident until you have the card.
With such an approval letter, you are not illegaly in Germany.
§ 81 (4) Applying for the residence title
If a foreigner applies for an extension of his or her residence title or for a different residence title before his or her current residence title expires, the current residence title is deemed to remain in force from the time it expires until the time of the decision by the foreigners authority. This does not apply to visas issued in accordance with section 6 (1). If the application to issue or extend a residence title was filed too late, the foreigners authority may order that the previous residence title remains valid in order to avoid undue hardship.