An Atlas V can get 400kg to the nearest star (well any star) by launching on a solar escape velocity -- see New Horizons. An expended F9 has a similar payload I

An Atlas V can get 400kg to the nearest star (well any star) by launching on a solar escape velocity -- see New Horizons. An expended F9 has a similar payload I think. You'd have to construct a container that would survive a failure - so an explosion of the rocket (on the pad or during launch), or a failure in LEO where it would have reentry. That container would then need to be able to be recovered no matter where it landed on that failure -- so things like floating would be important, and some form of control over landing so it didn't crash onto someones house. Or in an inconvenient country. Obviously it has to stay in one piece. Now sure, much of that shielding doesn't need to go beyond LEO, but it leaves very little room for the actual payload.