Under what circumstances may contract work be performed even though
the fully executed contract has not been received?

If this is work being done for the government (which I'm guessing it
is from reading another question of yours), then doing any work
without a contract is risking not getting paid for the work.
The only money you'll get is money that has been obligated by the
agency you're doing work for... it's likely that they will obligate
the money for you if you're doing the work they want done, but you
can't bank on that until you see the official contract.

You would be wise to consult a business law attorney about this. 
Let's hope that you have some type of documentation where one party
agreed to hiring your services and did you give a price quotation? 
You can partially protect yourself by not doing business until the
other party at least gives you a purchase order.

4KEITH (I'm NOT a GOOGLE Researcher)
Accountant