As in eliminate cash entirely? Not as far as I know. Even in Sweden, articles I've read suggest that the shift to cashless will continue at its own pace but no one is really talking about completely pulling cash out of circulation at this point. (And most people don't seem to be in favor of that.)

What probably does happen over time though is that, if the cashless penetration becomes high enough, a lot of retail merchants and individuals just stop accepting cash because it's too big a hassle for a tiny slice of their business.