CDS and other insurance instruments will be exercised when Greece defaults, if it has not done so already. When that occurs, the CDS issuers will likely initiate lengthy legal battles to prevent and delay payouts, because the amount of CDS insurance which they have sold appears to be far greater than can be covered. The value of bonds insured far exceeds the value of bonds in existence. Default pay-outs might far exceed the default losses. Should that be the case, to avoid bankruptcy the CDS issuers will need to prevent pay-outs. The legal system is the likely battlefield. G20 governments, which now largely back those insurers, will likely support those legal efforts to prevent or delay CDS pay-outs.
CDSs probably can no longer be relied upon to insure bonds. With the insurers facing bankruptcy, governments would insure those insurers.
See Seeking Alpha's primer on CDSs for general information about systemic risk created by the unregulated CDS market. See Nomura's primer for more information about the workings of CDSs under various credit events.
I thank JSMineset for commentary on this matter.