What does “hopefully yours” in a letter mean, and when is it appropriate to use it?

Question by CaseyF: What does “hopefully yours” in a letter mean, and when is it appropriate to use it?
I’ve seen a bunch of people end letters and emails with:

Hopefully yours,

Name

What is that supposed to mean?
Like, if someone uses “Best Regards” that means that they are giving you their best regards.
And if someone uses “Yours Truly” it implies that what they have written is sincerely “yours”

So, when would you use the closing “hopefully yours,” and what does mean, literally?
Is it even a real letter/email closing?

Best answer:

Know better? Leave your own answer in the comments!