Two scenarios:
If no one spends bitcoin, and miners refuse to sell/hoard bitcoin, the price will go up. This is supply restriction.
If no one spends bitcoin, and miners dump on exchanges trying to make ROI, the price will go down. Supply has increased and there is less speculative interest, or demand. This is demand restriction.
This is the beauty of bitcoin however; if the price gets too low, miners will stop mining and difficulty will decrease, enticing more miners to join. Inversely, price gets ahead of itself and miners will dump, bringing the price back down to earth.
I am too sure and I too do hope that it's the supply restriction that's going to happen because it does sound a lot better than the other you stated. But supply restriction is totally different from people not spending IMO. Because, how long some people will be able to hoard, they will start spending it for any simple reasons too. So, long term consequences are not possible form these, I believe.