Actually, Alaska is one of two states that completely stopped state funding of its public radio and TV system within the last ten years. The other is New Jersey.
Let's take the case of New Jersey first. The state had a statewide public radio network in 2012. When state funding for the network was abandoned, WNYC-FM took over the running of the public radio stations in northern New Jersey with Philadelphia's WHYY-FM taking over the stations in the southern part of the state. WHYY-FM recently sold two of its southern New Jersey affiliates to religious outfits (one was in Bridgeton, and I do not now recall where the other one was.) While the stations in the north have continued with some separate programming from that of WNYC-FM, the latter has dropped webcasting of that northern New Jersey programming. There was a third station that got New Jersey state funding in the Asbury Park area that was not part of the state's public radio network. When the state funding was halted, that station dropped all NPR network programming and is today a 24-hour aday adult album alternative station.
Alaska, unlike New Jersey, never had a statewide public radio network. Someradioguy will probably correct me here, but I believe the only program that was being carried statewide by all Alaska public radio affiliates produced insite the state was "Alaska News Nightly,", a news program dedicated to the state of Alaska. As of this riting, that program is still being aired. What the three biggest Alaska radio stations (in Anchorage, Fairbanks, and Juneau respectively) have dropped because of state funds no longer being available are their HD channels.
IF CPB funding is fully cut, I do not expect the state of Alaska to pick up the slack. The state's reasoning for getting out of supporting public radio outlets is the same as the reason at the national level.
New Jersey may or may not prove to be a different story. The state is currently being governed by the minority party in Washington, D.C. and may, if budgets allow, provide some support to its remaining public radio outlets, but it probably will not be enough to offset what those stations will lose in CPB funding. Put another way, if the CPB funding is cut, both WHYY and WNYC-FM will be selling more of the stations in their respective networks.