Keep field empty if the product of two fields is equal to 0

You should use this script as a "Custom Format Script" instead of a "Custom Validation Script" because the Format script only modifies the display in the field, it does not change its real value which is always zero and therefore remains usable for further calculations.

As validation script of that field use this:

if(event.value == 0)event.value = "";

Can you clarify?

At the moment you get an error or some indication that something is missing if the other fields are not completed?

That seems to be some scripting requirement.