It depends on how the PKG was downloaded/installed.
If the PKG was created or downloaded in background as a bubble, then the file stored in /dev_hdd0/vsh/game_pkg
Once the package is installed, the bubble files are deleted automatically from the system. If you don't have a backup of the package, you need to re-download the file if you want to install it again.
If you downloaded and placed the file manually in /dev_hdd0/packages via FTP or with a File Manager, then the PKG file remains in the original localtion and it must be deleted manually.
IIRC multiMAN downloads the PKG to a subfolder (I don't remember the name) in /dev_hdd0/game/BLES80608/USRDIR, then it redirect the folder in memory so it can be installed from XMB.
If the system is turned off during the installation of a PKG, the extracted files remain wasting disk space in /dev_hdd0/game/_INST_<timestamp>
Sometimes the PKG are installed first as DLC or game patches with a version higher than the original game. In these cases the game files could already exist, but not shown on XMB because the game was not installed in the correct order. To solve this, go to /dev_hdd0/game and delete the folder corresponding to the TITLE ID of your game. Then reinstall the game in the correct order.