If you want people to respond to your questions, you will need to provide more information :
Where did you find out about a connection between fasting and liver dumps ?
Which drugs are you referring to ?
Unless we know how someone makes a connection, we can't answer your question about very low-carbing.
It's only your brain that has a glucose requirement. Your body producing it in the absence of carbohydrates is not going to greatly increase your blood sugar, so that's all I can say for now.
Geoff