While I understand you situation is a bit different (a local public TV station changing hands to become a commercial station?), I can tell you what happened here in Los Angeles when KCET, the huge momma flagship DUMPED PBS to become a NON-PBS member public TV station: Dish continued to provide the station in LIL HD and still does, if that info helps.
Some stations before KCET dropped PBS and more stations after KCET have DUMPED PBS. PBS's current formula for extracting $$$ payments to support the network can be quite onerous and some stations either can't take the financial drain or sure as hell resent it as PBS refuses to consider situations that some stations in some markets face, such as several other PBS stations in the same market cutting into one stations revenue.
Frankly, PBS and all public TV stations are owned by every single American, and because of this I believe that the PBS national feed should be provided to all MVPD's for resale (usually a few dollars) to any subscriber who wants it. Of course, the local stations would CRY, but the current system of distribution is anachronistic and and many markets do not air ALL of the PBS programming and PBS National Feed holds pledge drives for itself (PBS) anyway. Most, yes MOST of the highly popular entertainment programming on public TV today comes from 3rd parties--NOT PBS--such as American Public Television. PBS is king of public affairs programming, but few stations air all the PBS public affairs programming, anyway, as just about all the documentary content (from 3rd party producers who also sell the same film to MVPD channels on cable and sat) and some science programming is not commissioned by PBS, anyway. PBS is now nothing more than NewsHour and Travis Smiley, Clay Aiken, endless David Foster pop concerts sequels crowding out any of The Met performances such that PBS has turned into a parody of itself. This is also why an increasing number of public TV stations say, "buh bye" to PBS. History, Science, NatGeo, NatGeo Wild, and Animal Planet are just a few channels that have superior science and nature programming than PBS as the same producers (mostly BBC and other UK producers) who USED to supply exclusively to PBS can now be found ONLY on MVPD cable or sat channels.
As much as the NewsHour is a great broadcast and the Metropolitan Opera (many live opera performances on Ovation, anyway), I can't say that I would miss PBS should it die compared to how I would have sorely missed it 20 years ago.