H4's non-worker social security number?

I'm a H1B visa holder. My wife just came in US with a H4 visa. I knew that as a H4 visa holder, my wife is not eligible for work as well as a social security number. However, last week, by change, an officier told us that my wife might be eligible to get a non-worker social security number and in this way we can save on certain fees. The offcier did not give us more info.. I just wonder if any of you have some idea on this non-worker social security number thing. Thank you.