The result of my Rubella IGG is 0; negative. What does this mean?

That means a person. Needs to get an MMR shot. The MMR vaccine will cause a person to form antibodies against Rubella virus and become protected against Rubella (German measles). The company that makes the vaccine stopped making the single-ingredient Rubella vaccine, so one has to take the 3-ingredient MMR vaccine.
You/or a baby risk. This test means you have no evidence you ever had Rubella or the vaccine. You could get Rubella if exposed. If you were carrying a baby at the time it could be aborted or end up deaf/mute/blind . Time to get vaccinated.