I loved The Family! It had a lot of twists and was really well done. Super bummed about that.
And I'm obsessed with Nashville so I really don't get that one - people are trying to protest but does that ever work?!
No, sadly they don't. Yes shows are sometimes picked up by another network or go to streaming, but it's not because of fan protests.
There's a lot that the average viewer doesn't understand about ratings and the decision to cancel shows. If anyone is interested in understanding more of it, I recommend The TV Grim Reaper (formally known as the Cancellation Bear). Throughout the season, he predicts renewals and cancellations and he explains why. He has a really good record. The best at predicting that I know.
For example, this year's results for him were:
CBS: 21-2-1
ABC: 22-3
NBC: 18-0-2
Fox: 14-2-2
CW: 8-2-2