According to the File System Hierarchy Standard, the lost+found directory is used for:

Files with unknown owners still have valid directory entries and inode references; ownership is a permission attribute separate from the filesystem link count that fsck checks.

The /proc virtual filesystem exposes kernel and process information dynamically at runtime and has no relationship to lost+found or fsck recovery.

The find command is a user-space search utility and does not write discovered files into lost+found; it only reports results to stdout.

When fsck (filesystem check) runs and finds inodes that are not referenced by any directory entry - known as unlinked files - it places them in lost+found for manual recovery. Each filesystem has its own lost+found directory, and fsck uses the pre-allocated space there to reconnect recoverable data that would otherwise be lost after an unclean shutdown or corruption event.