Music library deleted from iPhone
Apple doesn't back up music files as part of iOS backups since they either came from iTunes Match / iTunes in the Cloud or they came from a computer.


You should try a tool like PhoneView to see if the files are still on the storage and just the catalog has become missing or corrupt.
You could reconnect it to the computer that has the music.
You could reconnect it to the cloud music.
You could pursue data recovery on the device itself - that would likely be extremely expensive or you'd have to be very lucky and have the device jailbroken and no further usage of the storage since each time a new file gets written, it can and will over-write the music.


If the music was truly on the phone, then it would be best to get a quote from a data-recovery specialist and then see if you want to try DIY recovery and/or if it would be cheaper to get the music elsewhere.