A frugal install just copies all the files on the Live CD to a folder on the hard drive. Other than that it is exactly the same as the live CD.
So if you don't have a save file on the hard drive, it will behave exactly like the live cd, and no files will be saved to the HDD.
If you want to save your changes (home directory, installed PETs and DotPups, network and X configuration), you should create a save file on the HDD when you shut down. If you boot puppy from any media (cd, usb stick, HDD), it will find it and use it, updating any changes back to the save file when you shut down.
Hope that helps!