What does a logic gate output when powering down?
Technically speaking, IC interface pins are formally "undefined" if power conditions are outside specifications. And the power-down transition is one of this cases. Therefore, your thinking is right, the receiving end cannot rely on the transient state of input pins. The interface must be protected from brown-out and glitchy conditions at the receiver end. Some interfaces (as eMMC and SD) do specify the power-off transition sequencing, which may not be easy to meet, and various pull-downs must be employed to meet these specifications.