This is a very good question, and one that is kind of tricky. Let's go through this step by step:
try
{
throw new Exception("From Try");
}
catch
{
throw new Exception("From Catch");
}
In the code above, Exception("From Try") is thrown and caught by the catch clause (pretty simple so far). The catch clause throws an exception of it's own, which normally we would expect (because the catch is nested in a larger try-catch block) to be caught immediately, but...
finally
{
throw new Exception("From Finally");
}
The finally clause, which is guaranteed to (try to) execute, comes first, and throws an exception of it's own, overwriting the Exception("From Catch") that was thrown earlier.
"A common usage of catch and finally
together is to obtain and use
resources in a try block, deal with
exceptional circumstances in a catch
block, and release the resources in
the finally block" - MSDN Article
Following this train of logic, we should try our best to refrain from writing code in our catch and finally blocks that is exception-prone. If you're worried about situations like the one you presented cropping up, I'd recommend logging the exceptions and their related information out to an external file, which you can reference for debugging.