At some point in time (past or future, or magically also present), a star passed in very close vicinity to our sun. It had a habitable planet in its system, full of alien plant and animal life. For the brief moment it was Δv-accessible, it was studied, and eventually colonized. The people going there knew it was going to be a one-way trip, as the star eventually moved further away. Possible stories to set before, during, or after encounter (or even long, long after).
(This works for no-FTL, hard sci-fi setting. By "very close vicinity" I mean, close enough for us to reach it via sublight propulsion, but still far enough not to mess up the inner Solar System gravitationally.)
--
EDIT: Wow, turns out this isn't even that implausible - https://news.ycombinator.com/item?id=18123098.