You shouldn’t. An access violation is a serious problem: it is an unexpected attempt to write to (or read from) an invalid memory address. As John already clarified, the unmanaged DLL might already have corrupted the process memory before the access violation has been raised. This can have unpredicted effects on any part of the current process.
The safest thing to do is to possibly inform the user and then immediately exit.
Some more details: An access violation is an OS exception (a so-called SEH or structured exception handling exception). This is a different kind of exception than the managed CLR exceptions from
System.Exception. You will rarely see SEH exceptions in purely managed code, but if one occurs, e.g. in unmanaged code, the CLR will deliver it to managed code where you are also able to catch it1.
However, catching SEH exceptions is mostly not a good idea. Further details are explained in the article Handling Corrupted State Exceptions in MSDN magazine where the following text it taken from:
The CLR has always delivered SEH exceptions to managed code using the same mechanisms as exceptions raised by the program itself. This isn’t a problem as long as code doesn’t attempt to handle exceptional conditions that it cannot reasonably handle. Most programs cannot safely continue execution after an access violation. Unfortunately, the CLR’s exception handling model has always encouraged users to catch these serious errors by allowing programs to catch any exception at the top of the System.Exception hierarchy. But this is rarely the right thing to do.
1This was true until .NET 3.5. In .NET 4 the behavior has been changed. If you still want to be able to catch such kind of exceptions you would have to add
legacyCorruptedStateExceptionsPolicy=true to the app.config. Further details in the articled linked above.