A better way to prepare for the device loss or failure, is by setting up a multi-sig wallet with redundancy, then you'll automatically have several copies of private payments on multiple devices.
Suppose I have multisig 1 of 2, but during transaction only first wallet is online, and just after receiving dark byteball, is lost.
Do I have access to those dark byteball using only second wallet(device)?
Good question.
Chances are high, you have. As soon as the first device receives blackbytes, it immediately forwards the private data to its cosigner(s) in the multisig wallet (the second device in your example). The data is sent through a hub, not directly, so it is no problem that the 2nd device is offline. The hub is supposedly always online, it accepts the data (end-to-end encrypted, so the hub can't know what this data is about) and stores it until the 2nd device comes online. When it happens, the 2nd device downloads the data and can spend blackbytes, even if the 1st device is already dead.