Linking 2 PIC chips

Hi, Ive got 2 circuits and each has a PIC chip on it. The circuits need to communicate using only standard IO pins. I have 10K resistors between them.

The chip work fine when both circuits are powered but if i turn one circuit off then the power coming into the input pin from the other circuit keeps the chip powered. Sometimes it just keeps an LED on another pin lit but very dim. Sometimes the chip will keep executing code. Is there a proper way to connect PICs accross multiple circuits? Would a different resistor solve the problem or do i need to use optos?

Im hoping for a small solution like a different resistor since ive already made the PCBs :(

Maybe you can use brown out reset .. have you measured the VDD voltage when only one pic is powered properly?

No, my multimeter isnt very accurate. The problem seems to be that the chip is getting its power through the LEDs which are connected to the same ground. I had a similar problem before where a ground wire was completely missing on a PCB and the chip could power itself through the IO pins. The resistors i added worked on some circuits but theres 1 PCB that is still causing a problem. The only difference i can think of is that this box has some LEDs which connect using common positive and its those LEDs which seem to be supplying the power to the chip. Thats weird since the PCBs have a shared ground and the only positive is going through a resistor into an IO pin (nothing else)