/usr/include/plymouth-1/ply/ is in libplymouth-dev 0.9.2-3ubuntu13.
This file is owned by root:root, with mode 0o755.
..
/usr/include/plymouth-1/ply-boot-client/ply-boot-client.h
/usr/include/plymouth-1/ply-boot-client/ply-boot-protocol.h
/usr/include/plymouth-1/ply-splash-core/ply-boot-splash-plugin.h
/usr/include/plymouth-1/ply-splash-core/ply-boot-splash.h
/usr/include/plymouth-1/ply-splash-core/ply-device-manager.h
/usr/include/plymouth-1/ply-splash-core/ply-keyboard.h
/usr/include/plymouth-1/ply-splash-core/ply-pixel-buffer.h
/usr/include/plymouth-1/ply-splash-core/ply-pixel-display.h
/usr/include/plymouth-1/ply-splash-core/ply-renderer-plugin.h
/usr/include/plymouth-1/ply-splash-core/ply-renderer.h
/usr/include/plymouth-1/ply-splash-core/ply-seat.h
/usr/include/plymouth-1/ply-splash-core/ply-terminal.h
/usr/include/plymouth-1/ply-splash-core/ply-text-display.h
/usr/include/plymouth-1/ply-splash-core/ply-text-progress-bar.h
/usr/include/plymouth-1/ply-splash-core/ply-text-step-bar.h
/usr/include/plymouth-1/ply-splash-graphics/ply-animation.h
/usr/include/plymouth-1/ply-splash-graphics/ply-entry.h
/usr/include/plymouth-1/ply-splash-graphics/ply-image.h
/usr/include/plymouth-1/ply-splash-graphics/ply-label-plugin.h
/usr/include/plymouth-1/ply-splash-graphics/ply-label.h
/usr/include/plymouth-1/ply-splash-graphics/ply-progress-animation.h
/usr/include/plymouth-1/ply-splash-graphics/ply-progress-bar.h
/usr/include/plymouth-1/ply-splash-graphics/ply-throbber.h
/usr/include/plymouth-1/ply/ply-array.h
/usr/include/plymouth-1/ply/ply-bitarray.h
/usr/include/plymouth-1/ply/ply-buffer.h
/usr/include/plymouth-1/ply/ply-command-parser.h
/usr/include/plymouth-1/ply/ply-event-loop.h
/usr/include/plymouth-1/ply/ply-hashtable.h
/usr/include/plymouth-1/ply/ply-key-file.h
/usr/include/plymouth-1/ply/ply-list.h
/usr/include/plymouth-1/ply/ply-logger.h
/usr/include/plymouth-1/ply/ply-progress.h
/usr/include/plymouth-1/ply/ply-rectangle.h
/usr/include/plymouth-1/ply/ply-region.h
/usr/include/plymouth-1/ply/ply-terminal-session.h
/usr/include/plymouth-1/ply/ply-trigger.h
/usr/include/plymouth-1/ply/ply-utils.h