In the U.S., where NPR News/Talk, Classical and AAA stations have lost federal funding, they've made it up with on-air fundraisers and donations, even if the license is still held by a state organization or university.
I'm not sure why CBC Music / SRC Ici Musique couldn't appeal to listeners for funding. And the CBC / SRC main radio networks have very good ratings and could either go with some limited commercials or similar on-air fundraising like NPR stations do in the U.S. No need to sell the stations.