You can put it on the resume anyways and as long as you are able to describe how you would do it and field questions about the idea, no one really will fact check too hard.
I honestly do that. If I have an idea that I know will be near-impossible to get through the internal politics and that likely nobody will really care about (like the saving 50k example), I put the idea on my CV as if I actually implemented it. I get asked about it at interviews and just fantasize about what would have happened had I done it. People tend to be mighty impressed. I tend to choose under-the-radar things that my boss wouldn't necessarily know about.