Not sure what will happen to our funds if OpenLedger goes down that is used by decentralized exchange BitShares.
In the case of centralized exchanges, you can read about Mt. Gox and BTC-e crack down.
I do have small amounts on exchange to buy stuff but I move it to cold storage even if it is small stuff. Hope this answers your questions.
OpenLedger is just a frontend to Bitshares. You can use bitshares wallet or rudex and it will all still work as long as Bitshares is up!