I was curious about this hypothetical situation.
If Yom Kippur would fall on Sunday, Motzei Shabbat, so immediately when Shabbat ends, Yom Kippur starts. Would there be some sort of separation, בין קודש לקודש, as we have when Yom Tov is Motzei Shabbat (in Shmoneh Esrei and Kiddush)? Would we light candles?
The core of the question is, which has a higher kedusha?
On the one hand, Yom Kippur is called שבת שבתון, while Shabbat is only called שבת. On the other hand, we have 7 aliyot on Shabbat, and only 6 on Yom Kippur.
This question may actually become practical when we return בע"ה to the Sanhedrin setting each month's calendar.