In the west this is still growing, but in Japan at least, it's way more common, at least regarding 'light novels' (kinda of like YA?). I'm not sure about earning money through subscriptions, but there people who write to those sites (similar to Wattpad) often struck a deal with a publisher to adapt the 'web novel' to a 'light novel'[0]

Edit: I know that for webtoons (korean comics) subscription is turning into a reality, at least in English markets. Not sure about how's it in Korea though

[0]: https://www.reddit.com/r/LightNovels/comments/6hgw1w/konosub...