For instance, your virtual machine has a host name "albert". When your main (physical) machine is online, "albert" can be pinged as usual. But when you are coming offline, "albert" can no longer be pinged. The explanation is simple -- there is no local network between your physical machine and "albert".
In order to enable such a local network, you would need to go to menu "Virtual Machine->Virtual Machine Settings". Switch to "Network Adapter" in the left frame and choose "Host-only" in the right frame. In this case it does not matter if your main physical machine is online or offline -- you will be able to ping "albert" and access internet from it.