Quoted from barakandl:There is an weird thing with these NVRAMs where they can work or mostly work even if the Vcc pin is not powered. Its like it can suck off power from the address or data pins enough to do read and writes.
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It does - but you can't rely on this method to provide reliable power.
Many devices such as these have clamping diodes on the inputs. This shunts input voltages higher than Vcc to the internal Vcc -- essentially providing some power to the device. Second diode clamps voltages less than zero to ground. Attd image shows how this works (image shown for 3.3V part but same principle for 5V part). These are intended to clamp small spikes often seen during switching between high & low, they are pretty wimpy diodes and it doesn't take much to destroy them.