They have multiple copies on multiple disks, on multiple racks, on multiple places (geographic redundancy).
Usually a private cloud will have a high availability system which one is master, the other slave and when one breaks, the other takes control. Some will have a Disaster Recovery plan in which they will have 3 systems just in case, and so on and so forth.
I was fortunate enough to have a project with a bank for Cloud services, and they have this information stored on high tech facilites, in a ground where no earthquakes are big, thick walls, redundant cooling, energy systems, arm guards in order to avoid breach, super systems monitoring digital attacks, and a large etcetera. They are guarding financial data, one of the most critical mission information one could ever think of, and so far, data is safe.
Our humble music libraries (even the biggest collector with 1 million albums) is pretty much safe that nothing will happen to their data. And before anyone says that hackers have stolen millions of stuff, let me remind you that those cases are because the security put on those Data Centers were not up to the task.
If a disk is broken, they open the rack, hot-swap the disk (no turning off of any equipment), change it, then the disk replicates and then the disk is operable, no data loss.
In my personal case, I will keep relying on Data Centers for my info, including my music, plus I will keep having my streaming services (if data is lost, its their responsibility not mine haha), and storing my local media in my computer, and in two or three different storage hard disk, just in case.