From the same article: "There are very few good uses of resurrection, and you really should avoid it if possible."
The best use I can think of is a "recycling" pattern. Consider a Factory that produces expensive, practically immutable objects; for instance, objects instantiated by parsing a data file, or by reflecting an assembly, or deeply copying a "master" object graph. The results are unlikely to change each time you perform this expensive process. It is in your best interest to avoid instantiation from scratch; however, for some design reasons, the system must be able to create many instances (no singletons), and your consumers cannot know about the Factory so that they can "return" the object themselves; they may have the object injected, or be given a factory method delegate from which they obtain a reference. When the dependent class goes out of scope, normally the instance would as well.
A possible answer is to override Finalize(), clean up any mutable state portion of the instance, and then as long as the Factory is in scope, reattach the instance to some member of the Factory. This allows the garbage-collection process to, in effect, "recycle" the valuable portion of these objects when they would otherwise go out of scope and be totally destroyed. The Factory can look and see if it has any recycled objects available in it's "bin", and if so, it can polish it up and hand it out. The factory would only have to instantiate a new copy of the object if the number of total objects in use by the process increased.
Other possible uses may include some highly specialized logger or audit implementation, where objects you wish to process after their death will attach themselves to a work queue managed by this process. After the process handles them, they can be totally destroyed.
In general, if you want dependents to THINK they're getting rid of an object, or to not have to bother, but you want to keep the instance, resurrection may be a good tool, but you'll have to watch it VERY carefully to avoid situations in which objects receiving resurrected references become "pack rats" and keep every instance that has ever been created in memory for the lifetime of the process.