Use of Power Pins in ICs
First things first. Some ICs do consume power even if they are not doing anything, check Diode logic and transistor-transistor logic ICs (1) (2). 

Secondly. The power pins are not only used for "power". They are also used for ESD protection. So if one of the inputs were to be higher than they were supposed to, it will get "shorted" to the power supplies. Link (3) "shows" a simple ESD protection circuit/diode. [This is the reason you might be able to use your ICs even though there is no power; it is because your inputs are "powering" the power supplies ]

Thirdly. Vdd and Vss [or Vcc and Vee for TTL ICs] set your noise margins. Therefore, You need a constant voltage reference to tell what is a logic low or a logic high, even if you do not draw any current!

(1): https://en.wikipedia.org/wiki/Transistor%E2%80%93transistor_logic

(2): https://en.wikipedia.org/wiki/Diode_logic

(3): https://en.wikipedia.org/wiki/Transient-voltage-suppression_diode