In Hyper-V on Windows Server 2016, .vmrs files store the running state of virtual machines (VMs). When a VM is up and running, the size of the .vmrs file is equal to that of the configured RAM of the VM. When you back up the VM, the Hyper-V Volume Shadow Copy Service (VSS) writer also returns the .vmrs file as the file to be backed up.
In this situation, when you do incremental backups, the actual incremental data may be much less than the actual data that's being backed up. For example, when the size of the updated data is 5 GB, the actual data that's being backed up may be 105 GB if the size of the RAM that's configured for the VM is 100 GB.
This behavior is by design.
When you do a hot backup and don't back up the .vmrs file, it will be the same as having forced to shut down the VM, and you will lose unflushed writes and in-memory data. When you restore the VM, you may receive the message that resembles “The VM is shut down unexpectedly”.
Hyper-V writer suggests that backup applications protect the .vmrs file. Excluding the .vmrs file from backup may cause a VM to be powered off unexpectedly during a restore process.
Microsoft has confirmed that this is a problem in the Microsoft products that are listed in the "Applies to" section.