Your eeprom was powered by the protection network diodes in the clock 
and data pins, not via the pullups. You can power everything down and 
measure the junctions between your data and clock lines and +Vdd of the 
eeprom. Getting rid of such 'phantom' power supplies is a major chore 
when you build low power systems. If you do not deal with this then the 
system will be very susceptible to self erasure and other accidents 
(such as not resetting properly) when out of the lab.

Properly getting rid of all the phantom power possibilities is not so 
easy. ANY cmos io pin connected to the outside world is susceptible of 
being an unexpected power pin at some time or another (because all cmos 
pins have protection networks). Worse, it will even work with ac 
'caught' from the air or a wire loom. Don't ask me how I know this. Oh, 
and the 'power' pin can be an output, which usually cannot be filtered 
with a series high value resistor (the usual fix).

Peter

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