Some time ago I saw a problem from a partner team in Microsoft that an InvalidOperationException is thrown from WeakReference.IsAlive. WeakReference wraps weak GC handle implemented in CLR's Execution Engine (GC handle is also exposed by System.Runtime.InteropServices.GCHandle which supports not only weak handles, but other types too). A weak GC handle will be allocated and assigned to the WeakReference object when the WeakReference object is created. As described by Jeffrey Richiter, the weak GC handle contains pointer to an object, if the object is collected by GC, the GC handle will be cleared to NULL. Most of time WeakReference.IsAlive returns true or false to indicate whether the tracked object is alive. The check is based on whether the underlying GC handle contains a non-NULL pointer or NULL. Similarly, WeakReference.get_Target will return a valid object reference or null. But after the WeakReference object itself becomes unrooted and finalized, the underlying GC handle will be destroyed and any call to IsAlive or get_Target on the WeakReference object will throw InvalidOperationException in V1.X.
How would any method being called on a finalized object? Well, if one object O has a field WR as WeakReference, when O become unrooted and there are no other roots for WR, both objects are considered to be dead and will be put into F-reachable queue for finalization(check also check Jeffrey's article). Since there are no guarantee about order of finalizers (things are a little bit different for critical finalizer), when O's finalizer is executed, WR may already be finalized. Thus inside O's finalizer or after O is resurrected, it could call methods on the finalized WR. In the example I mentioned at the beginning, the problem is some object's finalizer is calling IsAlive on its WeakReference field.
The guideline for finalization says not to use any finalizable field in finalizer, so it's fair for WeakReference's properties to throw exception if they are called in finalizer. But it might be hard for people to understand why IsAlive needs to throw. After all it's only used to check status and doesn't need to access the tracked object if it's already collected. I think the reasoning is that IsAlive is meant to check whether the underlying GC handle tracks a live object, but if the GC handle is already gone during WeakReference's finalization, we can't answer the question.
The most interesting part is to look at history of this design decision. In V1.X, both IsAlive and get_Target property throws exception after the WeakRerence object is finalized; in Beta2 of V2.0, IsAlive still throws, but get_Target won't throw, it will return null after finalization; after Beta2, we made a change so that IsAlive won't throw either, it will return false after finalization. Partly because there are too many people calling WeakReference.IsAlive in finalizers, and it is not a really dangerous thing to do. Note that WeakReference.set_Target always throws after finalization.
So on CLR V2.0 offical released build, you could safely use WeakReference in finalizer.But it is still good practice not to use finalizable objects in finalizer, including WeakReference.