After switching to Ethernet Network connection on MacBook Air using Apple USB Ethernet Adapter, Network connection stops working both on the Mac side and inside the Virtual Machine.
The MacBook Air Ethernet dongle is a USB device and it can be accidentally connected to the Virtual Machine. If your Virtual Machine has Shared Network mode set in Configuration (by default) Network connection would be lost both on the Mac side an inside the Virtual Machine.
In order to get Network connection working on both sides and prevent this issue to occur in future, please follow the steps below:
Go to Parallels Desktop menu -> Preferences
Open USB tab and highlight Apple USB Ethernet Adapter in the list of devices.
Select Connect it to my Mac option and close Preferences tab.
Restart the Virtual Machine.