Don't look at it that way; look at it as the extinction of suffering.
The problem is that Buddhism is dealing with the ineffable, so any attempt to define these phenomena will be imperfect at best and a disaster at worst. Unfortunately, people have felt compelled to add details and in the process... well, your question is a classic example of the kinds of illusory problems people face.
First, you're obviously going to gain something out of Buddhism, otherwise why practice? If someone came to me, said that my finances were a wreck, but if I worked an extra job, someone ELSE would improve their finances, I wouldn't waste my time. So why is it different with Buddhism?
It isn't. However, the problem is that there are two different definitions of "self" that are being used in discourse, and it's not always clear which definition is in use. Thus semantic confusion reigns, creating illusory problems out of thin air -- nonsensical, utterly unimportant problems that prevent you from doing what Buddhism teaches you to do -- PRACTICE.
One "self" is raw consciousness. If you stub your toe, you will feel it. In that sense, that you does and will continue to exist.
The other "self" is the bundle of concepts that you identify with, the history and attributes that you think define "you". It's that you that won't exist and that's the source of your suffering.
Confusing the issue is the fact that the experience of the first kind of self's experiences can be transformed by one's conceptual filter (it's amazing how our perceptions are shaped by concepts), so that even that self -- while not vanishing -- also seems to be transformed. That stubbed toe that hurts may involve a lot more conceptualizations in the "physical pain" than you may think. This means that this first type of self would still feel the stubbed toe, but may not feel the pain of the stubbed toe, given how much of that pain is really conceptualization.
Does your head hurt yet?
A classic saying is "there is suffering, but none who suffers". On the surface, it seems to almost be a claim that suffering is a purely impersonal phenomena. In a way it is, but in a way it isn't. There's experiences that make up suffering, but it's those experiences when conceptualized with respect to the illusory (second type of) self turn those experiences into suffering. Which means there really is no suffering until we actually believe there is one who suffers (curiously circular, no?) so by eliminating the one who suffers, we eliminate suffering or the suffering of the one who suffered, who actually doesn't really exist, but does in a way.
Ok, NOW does your head hurt?
That's the thing; when we run into so many difficulties that half our time is spent trying to duct tape the holes in our conceptual edifice, it's a sign that we are thinking about the problem in a fundamentally wrong way.
Buddhism itself seemed to notice this and in (what I take) to be a rare moment of lucid self-criticism, it offered the Fetters of Views and Parable of the Poison Arrow teachings. The idea is to avoid the temptation to conceptualize and instead practice. If things get better, don't over-think it. Just do what works.