MtGox's secondary market
MtGox, the poster child of why one shouldn't trust exchanges with one's BTC, has officially shut down in 2014. However, months before that you could already see some red flags popping up that something was going wrong. MtGox started having some fiat withdrawal problems, and as a result, its market was off by 10+% and ripe for arbitrage. Some people could make a tidy profit churning money around, provided they could get their fiat out of the exchange.
A few months later, the situation got worse - MtGox has officially halted both its bitcoin and fiat withdrawals altogether. However, probably due to some interesting code optimisation, someone figured out that if you withdraw bitcoins straight into a deposit address of another MtGox account, the funds would be transferred without creating a transaction on the blockchain. It looked like that functionality was governed by the "MOVE" API call, rather than "SEND". This tiny functionality was enough for someone to build an entire secondary market for MtGox before the whole exchange went under.
While I can't find any reference to what the site was (EDIT: the website was Bitcoin Builder, as pointed out by /u/samurai321), as the news of MtGox collapse has probably buried it in the sands of time, I remember it being a simple BTC-MtGoxBTC exchange. One could deposit actual bitcoins and trade them for bitcoins owed by MtGox that were moved to the secondary market's address. It allowed some people to get rid of their coins frozen at the exchange and cash out to the safety of the wallets their own, while letting others speculate on whether or not MtGox would be going under. I remember seeing the price reaching a level of 30+% discount on the market, which is fairly comparable to the current Bitfinex scenario...
Decentralised secondary markets
After MtGox collapsed, I haven't seen a similar secondary market pop up anywhere. The closest thing that comes to mind is being able to trade Bitstamp's IOUs on Ripple, which might be an ideal approach for trading exchanges' debt (at least provided the exchange doesn't run into new hacks). If Bitstamp was to go under, you could still trade about 1.5M USD and 2k BTC of its issue on the decentralised exchange nearly indefinitely. Figuring out its USD-USD and BTC-BTC exchange rate against an operating pool could be a clear gaige of confidence in the platform - if there were talks of the exchange recovering, the price might get closer to parity, or go away from it in the opposite case.
At the same time, such a secondary market might be used for something more morally muddy...
Buying one's own debt
Say Bitfinex's tokens were tradable during the hack. Before everyone knew how much was lost percentage-wise, the market would be wild with speculation - you probably could buy bitcoins at 50+% discount, perhaps even at 90% discount if the fear would set in. Now, if Bitfinex was aware of such a situation and knew how much deposits they could actually cover, they could try buying up their own debt for pennies on the dollar before the haircut was to take place. This could allow them to buy off some of their debt at a discount, reducing their obligations to their customers and therefore creating a theoretical profit.
Such a scenario would be highly unethical and I would guess highly illegal, but I wouldn't be surprised to see something like this happen sooner or later in the Bitcoin world. Instead, let's imagine some more ethical approach Bitfinex could act on their current situation...
Slow debt repayment
I'm not sure how Bitfinex structured their token program as I don't use the exchange. However, a good approach to eventually righting everyone would be for them to convert everyone's BTC balance into those tokens. At any time, the users would be able to cash the tokens in and get actual coins, minus the haircut. With each token converted, their obligations would decrease.
The tokens would also be tradable on the exchange itself for actual coins, creating a market for the debt. Anyone wishing to speculate would be able to trade the coins for a value between the haircut discount and 1BTC. The price would have upper and lower bounds, but could fluctuate in between.
If Bitfinex was diligent and set on repaying the debt by eventually buying up all of the tokens, they could publicly declare their strategy of doing so - perhaps a portion of their monthly income would go directly into purchasing the tokens from the market at the spot rate. With every purchase, the amount of tokens in circulation would decrease, thus the ratio of their bitcoins earmarked for buying back the tokens to the actual amount of tokens would increase, making the haircut smaller and smaller. Gradually, the gap between the value of the tokens and the real coins would shrink so much they could convert the tokens themselves straight into coins at a 1:1 ratio and remove them entirely.
In the end, the amount of coins you would get back would rely only on how quickly you need them - you could get them today for 36% off, perhaps get them for 30% off in a year, or get a full amount in a decade. The market would decide what the future value of the tokens would be, and with each month (and perhaps with each trade if some fees were to be maintained for this market), the debt would be slowly repaid.
In the end, this is an optimistic scenario assuming the exchange could earn back millions of dollars worth of coins before the company would go under. Similarly, if you believe the value of bitcoins will go up, the debt may never be repaid - the value of the coins left to be repaid could be going up as the number of the coins would be going down thanks to the increasing price.
One way or the other, it would be a really interesting case study if Bitfinex was to implement something like this...