So the AU would be that the traveler dies and the crew of the enterprise D are left stranded at least two galaxies away from home. They can send a subspace message but it would take a long time for it to reach the federation. Basically Voyager without the slightest chance of getting home, how does the crew handle such vast distances? Does Picard try to get them back demanding Warp 9.99 and Geordie to work miracles? Or do they reluctantly settle down? Anyone interested?
The problem is that it is pretty much hopeless from a "let's start flying back" perspective. A galaxy itself is vast. Not only would they have to traverse the galaxy to get out of it, they would have to then travel between galaxies to reach the Milky Way, and there is nothing between galaxies except a vast empty blackness. So the ship (likely long past when everyone of the original crew is dead by the time they reach the edge) would have to have enough supplies and power on board to make a self contained centuries long journey. And then when they got there, they'd hit the Galactic Barrier. On the plus side, we'd have Eternal Captain Data. I think, more likely, they take the opportunity to explore the M33 galaxy, uncovering new knowledge, and seeking out a way that could return them home. And the fall back goal, if things go south, would probably be to just settle on a planet and make the best of it. Maybe the Enterprise-D would get kept in service, exploring nearby space for the new settlement, bringing supplies and help, and looking for some way to return home.