EDIT: After Joel Coehoorns excellent answer, I understand that I need to be more specific, so I modified my code to be closer to thing I\'m trying to unders
The life time of object B is longer that A, so A may be disposed earlier
It sounds like you are confusing "Disposal" with "Collection"? Disposing an object has nothing to do with memory or garbage collection. To make sure everything is clear, let's break up the two scenarios, and then I'll move on to events at the end:
Collection:
Nothing you do will ever allow A to be collected before it's parent B. As long as B is reachable, so is A. Even though A is private, it's still reachable from any code within B, and so as long as B is reachable, A is considered reachable. This means the garbage collector doesn't know for sure that you're done with it, and will never collect A until it is also safe to collect B. This is true even if you explicitly call GC.Collect() or similar. As long an object is reachable, it will not be collected.
Disposal:
I'm not even sure why you are implement IDisposable here (it has nothing to do with memory or garbage collection), but I'll give you the benefit of the doubt for the moment that we just don't see the unmanaged resource.
Nothing prevents you from Disposing A whenever you want. Just call a.Dispose(), and it's done. The only way the .Net framework will ever call Dispose() for you automatically is at the end of using
block. Dispose() is not called during garbage collection, unless you do it as part of the object's finalizer (more on finalizers in a moment).
When implementing IDisposable, you are sending a message to programmers that this type should (maybe even "must") be disposed promptly. There are two correct patterns for any IDisposable object (with two variations on the pattern). The first pattern is to enclose the type itself in a using block. When this is not possible (for example: code such as yours where the type is a member of another type), the second pattern is that the parent type should also implement IDisposable so it can itself then be included in a using block, and it's Dispose() can call your type's Dispose(). The variation on these patterns is to use try/finally blocks instead of a using block, where you call Dispose() in the finally block.
Now on to finalizers. The only time you need to implement a finalizer is for an IDisposable type that originates an unmanaged resource. So, for example, if your type A above is just wrapping a class like SqlConnection, it does not need a finalizer because the finalizer in SqlConnection itself will take care of any needed cleanup. But, if your type A were implementing a connection to a whole new kind of database engine, you would want a finalizer to make sure your connections are closed when the object is collected. Your type B, however, would not need a finalizer, even though it manages/wraps your type A, because type A will take care of finalizing the connections.
Events:
Technically, events are still managed code and shouldn't need to be disposed. However, there is an issue with events such that sometimes people like to use IDisposable with types that have events. The problem is that when a type X subscribes to events in another type Y, Y now has a reference to X. This reference can prevent X from being collected. If you expected Y to have a longer lifetime then X, you can run into problems here, particularly if Y is very long-lived relative to many X's that come and go over time.
To get around this, sometimes programmers will have type Y implement IDisposable, and the purpose of the Dispose() method is to unsubscribe any events so that subscribing objects can also be collected. Technically, this is not the purpose of the Dispose() pattern, but it works well enough that I'm not going to argue about it. There are two things you need to know when using this pattern with events:
In this case, your type A is private to type B, and so only type B can subscribe to A's events. Since 'a' is a member of type B, neither is eligible for garbage collection until B is no longer reachable, at which point both will no longer be reachable and the event subscription reference won't count. That means a reference held on B by A's event would not prevent B from being collected. However, if you use the A type in other places, you may still want to have A implement IDisposable to make sure your events are unsubscribed. If you do that, make sure to follow the whole pattern, such that instances of A are enclosed in using or try/finally blocks.