I can think of a few reasons why -
a) Local papers have gotten much of their revenue from subscriptions for a long time; their customers are used to this model.
b) Their ads are local, targeting perhaps a few thousand people at most. That makes a paper (with high penetration and trust in the target audience) a viable alternative to Google ads.
c) They provide news which doesn’t have a lot of alternative sources, while still being of interest to the readers. This encourages readers to keep subscribing (providing stable income), and the continuing subscriptions encourages advertisers to keep spending their ad dollars (or kroner, as it were) on the local paper.
Go to a city council meeting, and count how many news outlets stay for the entire thing. Most places, you're lucky if it's one. Even in big markets, you can probably count it on the fingers of your hand.