This is why exchanges with public asset lists are important (for example, BitFunder). Even if BitFunder suddenly shuts down, asset issuers will be able to know who owned what.
Ah yes, thank you for this link.
But I guess you also have to rely on the asset issuers themselves honouring the contracts made on any individual stock exchanges - ultimately they could just neglect to pay a dividend for 1 month. How would you enforce that? And without any formal contracts or if a stock exchange went down, how would you trade out of the stock at a future date?
Asset issuers can default at any time without needing the exchange to go down. In GLBSE's case the lack of any provision of investors' details provided a convenient window for issuers to vanish/claim ignorance (or do a Gigavps and charge a hefty fee for recognition of your claim - pricing smaller non-US investors out of their holdings). That excuse has gone with BTC.CO and (to an extent) Bitfunder (the asset list there is incomplete - as it only includes investors who opted in by providing a BTC address or ticking a box to allow sharing of their email address) but the capability for issuers to vanish is ALWAYS present and, without enforcement of contracts, can't be seriously mitigated.
All the time there are issuers there will be issuers who default. The rate of default/failure has to be factored in when deciding what rate of return is acceptable for investments (over-simplifying, if 10% of assets default/fail per 3 months then you have to make 11% profit per 3 months on the 90% just to break even - so anything paying less than ~ 4% per month should be ignored unless you have good reason to believe it's in the 90% not the 10%. Those numbers are illustrative not intended to be taken as fact - actual default/failure rate may be lower or higher: my money's on higher, dependent on how you define default/failure.)