The pins of most IC's probably including the HD44780 have protection diodes conneced to ground and their supply lines. They are there to protect the IC in case excessive voltage is put on a pin, the idea is they safely conduct the excess into either ground or the supply. If you remove the VDD connection, the supply line voltage drops below that of the signals on the pins so the diodes start to conduct and because they are connected to the internal VDD line, they supply power to it.
What you are doing is wrong though and can damage the 74HC164, PIC and the LCD. Those diodes are not intended to carry constant current, especially to the backlight which has quite a high demand and the shift register probably has it's outputs overloaded as well. The biggest danger is that when you reconnect the VDD you will get what's known as "latch-up" occurring. This is a state where the input stages of the LCD can go into a state where they draw very high current and potentially burn out. If you want to prevent the LCD showing anything, either turn off all the power to devices connected to it as well, or tie the read/write line into read state (high) so no data is written to it.
Brian.