APFS Container or Volume Corruption (macOS)
A Mac stuck at an unmountable volume or endlessly rejecting a FileVault password that used to work looks catastrophic, but Apple's APFS format keeps a built-in fallback that a lot of other file systems don't — if it's still reachable.
What's actually happening
Since macOS 10.13, APFS organizes storage as one physical "container" that can hold several logical volumes sharing the same free space, along with space-efficient snapshots and, on many setups, tight integration with FileVault encryption. An interrupted write, a forced shutdown mid-update, or a failing underlying drive can damage the container's own metadata structures rather than any particular file — which is exactly why the failure often shows up as the whole volume refusing to mount, or FileVault suddenly rejecting a correct password, rather than as a handful of missing files.
How recoverable this really is
APFS supports snapshots, and Time Machine can use APFS snapshots as part of its backup workflow. If a usable snapshot exists and the metadata needed to reach it is still readable, it may provide an earlier consistent view of the volume. But snapshots live on the same storage and share much of the same container infrastructure, so they are not independent backups and cannot be assumed to survive container damage. Where the container's core metadata is damaged, recovery becomes a file-system reconstruction problem rather than a simple snapshot rollback.
The general approach
If the data matters and the underlying device may be unstable, preserve or image it before attempting file-system repair. On healthy storage, Disk Utility's First Aid is the standard Apple repair path for APFS, but it is still a write-capable repair operation and should not be described as inherently non-destructive. Also check Time Machine and any available snapshots or backups before modifying the affected volume. Genuine container-level damage may require block-level analysis and reconstruction.
Running First Aid repeatedly after it reports it can't repair the volume doesn't help — a second or third attempt won't succeed where the first didn't. At that point, imaging the drive before anything else touches it is the more useful next step.
This is the macOS-specific version of the general problem covered in File System Corruption. For how Time Machine's local snapshots fit into a broader backup plan, see Backup Drive Picks.
This page describes the general situation, not a guaranteed fix for your specific case. If you'd rather have someone experienced take a look before you try anything, see what a hands-on evaluation looks like.