The general plot is that they indeed find a way to return to the normal world. And even better, to 'connect' the two worlds so people can travel between them.
To explain it in a little more detail:
Aliens have come to earth. Only these aliens live in the digital world. When they arrived, they happened to stumble across the elder tale game, and the game going online for the first time looked like an entirely new world was created just as they arrived. So they entered it. However this had unintended side-effects. Part of the physical world, and thus players that were online at the time the aliens entered, got pulled into the world as well. So eventually they find out about the aliens, and that it's possible to go back to the physical world. And maybe to even connect the two worlds through a portal or something.
Also, dying in the fantasy world does have a negative effect. You lose a memory every time you die, starting with the memories from the real world. Could be something as simple as what your room/apartment/house looked like. Or could be as serious as forgetting a family member. Though it pretty much always starts with less important memories. This happens because when you 'die' you get sent to the moon in that world. On that moon, there's a huge lake of some kind filled with memories. And if you want to resurrect, you have to offer a memory of your own to do so. Only you don't remember having been on the moon once you're alive again. And these aliens feed off of those memories as a kind of energy.
I didn´t think of this overarching plot myself by the way. It´s from an anime called "Log Horizon". (I recommend it if you like mmorpg's! :P) What has happened so far in between was mostly my own idea though.