I've a VM on a disk with I/O error, I want to make backup of that VM while it's running, therefor it's not possible to use dd,
Is that possible to ask vzdump to continue on I/O error of source disk?
You can try with ddrescue
But, of course you shouldn't do this while the filesystem is mounted (VM is running). If you want to save everything possible while the VM is running try to evacuate all the files from the VM by tar or rsync.