The short version: Mt. Gox stopped paying out USD-denominated claims, because (as was correctly perceived by many people) they were insolvent. They continued paying out BTC-denominated claims. The only way to get value out of Mt. Gox was to either go through yen (which the vast majority of customers couldn't do [0]) or buy Bitcoin and withdraw, which caused the price of Bitcoin to gallop upwards in late 2013.
[0] I got a number of interesting business propositions that year: https://twitter.com/patio11/status/423869016776933376