The government gets around this by ousting their target from their companies prior to laying criminal charges. Once the target no longer has control over their business, the new management can be pressured into dropping / denying the target's D&O coverage.
EDIT: Huh, it seems that although it's rare, yes, sometimes your D&O insurer will try to recoup costs by sending you a bill. Look at this: http://www.dandodiary.com/2012/11/articles/d-o-insurance/do-...
Interesting, the article says many (presumably non-criminal) securities cases settle because companies are afraid an adverse judgement would void their D&O insurance. I wonder if anyone ever pleads nolo contendere in a plea bargain just to maintain D&O coverage.
edit: Maybe it's time for lawyers to start accepting bitcoins for compensation?
Naturally the lawyers would have to figure out whether (or how best) you could do something like that in such a way that the money couldn't be seized.
To address your comment in detail:
1)>>>In short, people would take out the insurance right before they commit a crime so they didn't have to pay for their own defense.
2)>>>I don't see how the insurance company could survive in that environment, since the principle of insurance is that most people won't need it.
Point 1: Require the insurance to be delayed: you must pay into the insurance for X number of years before it can be used. In this case, "right before they commit a crime" will end up being long enough to recoup the costs of the defense. An actuary can help find what number of years is needed for the specific business.
http://en.wikipedia.org/wiki/Actuary
Point 2: All insurance companies are faced with the challenge of survival. They often overcome this challenge by increasing their pool of customers: "most people won't need it" and are profit centers, the few who do need it are the cost centers. Again, actuaries are the folks to call.