Lets see, I don't know any official fan subbed websites like the Japanese ones I listed, but here's a few that might work..
I know ALOT of C-dramas can be found on YouTube... https://www.youtube.com/@FreshDrama/playlists this channel has quite a few C-dramas. They have full length series and some snippets. There are so many other channels as well that give us dramas. Another way is to search up the title name episode number and eng sub, and the show could pop up. I know Dailymotion is free and safe to use as well.
Viki- This one's a common one but in case you didn't already know, they have ALOT of free stuff on there. Way back before I got my subscription, I used to watch my dramas there in the free option. (even tho there's commercials...lol) They might not have the popular stuff for free, but man do they have quite the collection. You're bound to find something good there. Some of my fav dramas are on there for free...
IQIYI- This one also has a wide selection of free dramas. And IQIYI is known for their Chinese dramas. So it has more Chinese than Korean. So if you're looking for Chinese dramas, IQIYI is the place to go. Umm same problem with Viki.. the most popular dramas people are watching are probably gonna be VIP, but it doesn't mean they don't have a good free collection. Just make an account!
Amazon Prime: I know they have some free K-dramas, I don't know about Chinese tho.. doesn't hurt to check it out..
There mightttt be some fansubbed websites like the Japanese ones I listed but I personally don't know any. You can ask the recommendation forum, and see if anyone knows any..