Question: The link between brain activity and qualia is unexplained. But most people think the former causes the latter.

What if its the other way, that our mind creates the external universe?
This does not necessarily mean that all other people are without a mind.
They also could have their own consciousness, but when they pass through this reality, we all create a 'Graphical Use Interface' which constructs a mental model. Our brain is part of this model, so when we die there is a possibility that our model of the world has died, but we have not.

Is there a way to eliminate this possibility?

(because this thought is unsettling; that I have to live through possible eternity)

Answer: 
Yes. You can eliminate that possibility.

First of all, what you are aware of as being "you" is the experience of being you. This is clearly separate from what you experience as external to yourself, because you aren't aware of creating things that you perceive as external to yourself. Could this generation of things be coming from some part of "yourself" that you are unaware of? Sure, in fact, let's assume that this is the case. We have at least two parts of you: the *experiencer* and the *generator*.

So you're asking about whether it is possible that this part of "you", the generator, will shut down, but the part of you that is the experiencer will keep on going? This doesn't make much sense. It seems far more likely that the generator (which may also create other experiencers like me for you to interact with) will keep going. After all, the evidence suggests that it was already here before you became aware of your experience.

But let's say it does happen, the experiencer continues and the generator shuts down. Well, now the experiencer has nothing to experience. Time is generated, so there's no time, space is generated, so there's no space. The experiencer won't even be able to think thoughts because there will be no experience of time to think them in. So there's no sense in which the experiencer will continue forever, because there's no longer a forever to continue into.

You could argue that there's some sort of external time that isn't being generated by the generator, but now you've broken the central premise that our minds generate external reality.
We first need to clear the widespread confusion between consciousness and mind.

It is the fact that the word "consciousness" is terminally ambiguous which led some philosophers to come up with the notion of subjective experience and qualia. We will follow this welcome innovation here.

We can define the mind as a sort of subjective representation of the world. Our mind is essentially qualia we take to be things in the so-called real world. Thus, we should distinguish the qualia from what qualia represent. We can see qualia as information, so that the mind has an information content. This information can concern anything, from memories of past events, to current percepts, thoughts, sensations, intuitions etc.

The most plausible and therefore reasonable assumption is that this information is somehow codified and stored by the brain, presumably through neuronal connections.

The crucial consequence of this is that the whole information content of our mind is stored in the brain, which also means that this information is quickly and irremediably destroyed when the person dies.

What might not disappear upon death is subjectivity itself, although this is totally speculative. Further, even if this is true, without the brain, there is nothing left to experience for subjectivity, at least nothing remotely similar to experiencing what it is to be a living human being.

It might also be that subjectivity is somewhat like space, ready to experience the information content of any living brain. This, however, is also totally speculative. Further, the information content associated with brains would still disappear with them, so that we would be unable to remember past subjective experiences.

These last two suggestions are possibilities in the sense that current science is not in a position to disprove them, but that does not prove that they are true. We just don't know. Further, even if they are true, they wouldn't amount to anything comparable to any of the various religious ideas about life after death.

The idea is that we can easily distinguish two things: the quality of our subjective experience and the information content of what we experience. The information content is really what specifies who we are at every instant of and throughout our lives. This is what most plausibly totally disappear upon death. The rest, subjective experience, or "consciousness" properly understood, would remain, but as a sort of blank screen. Not much to look forward to.