I'm not sure this totaly meets your requirement for a passive system, but I think its at least part way there and is a novel approach so worth a mention

What you need is a “vanguard” Think a very wide ultra-thin circular membrane together with minimal stabilisation and communications equipment traveling a long way ahead of the generation ship on exactly the same heading. If the vanguard is sufficiently far ahead there would be time for it to detect any rock passing through its membrane and give sufficient warning to the generation ship to fire emergency lateral thrusters to adjust course slightly and avoid the object.

A variation on this would be a small fleet of small probes fitted with wide angle laser projectors and detectors plus minimal communication and stabilization equipment. These could also fly far ahead of the generation ship in a wide circle and create a net of laser light that could detect any rock passing through and warn the generation ship in a similar way. If any of the probes were hit themselves the others could take over giving multiple redundancy. The other advantage would be the capacity to have a much wider net giving a greater safety margin.