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's local snapshots — the same mechanism Time Machine uses to keep hourly local backups on the same drive — are stored as a copy-on-write history within the healthy parts of the container, and they frequently survive damage that makes the current volume state unmountable. That means a volume Disk Utility can't repair outright sometimes still has a very recent, fully intact snapshot to roll back to. Where the container's own core metadata is damaged rather than a single volume's state, the situation is closer to general file-system corruption, or to RAID-style container damage on a Fusion Drive specifically, and is a harder job than a snapshot rollback.
The general approach
Try Disk Utility's First Aid first — it's purpose-built for APFS structural repair and is non-destructive when it fails to fix anything. Before assuming a repair is even necessary, check whether a recent local snapshot exists through Time Machine, since restoring from one can resolve this without any repair attempt at all. Genuine container-level damage beyond that generally needs the same block-level imaging and reconstruction covered elsewhere in this catalog for other file systems.
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.