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We have no idea how they could be traveling through space. They could be using something like the alcubierre drive which wouldn't be affecting by dust or microscopic things in space puncturing the craft, they'd just get warped around the craft with the rest of space.

Plus, space is so vast and lightspeed is so slow, I can't imagine plotting a trajectory to avoid stars/planets would be at all difficult for a society so advanced.

Have you ever seen those videos of someone getting their first fast car and immediately planting it in a building? Things that are made to handle well going very fast don't necessarily do well going very slow. It could be they normally depend on some guidance infrastructure for intra-stellar travel where they normally operate that isn't present here.

Maybe they just send a few trillion and hope a few make it