Do preamps have a damping factor or negative feedback? My layman's mind thinks that a line stage would not have much if any.
Virtually all solid state preamps use negative feedback. Many tube preamps do as well, but not all. For example, the new Raven preamp developed by Lynn Olson and Don Sachs that will be built and sold by Spatial Audio does not use any global negative feedback.
I have a BAT preamp that I am working on fixing (bought a broken one that the previous owner didn't want to deal with) that doesn't have negative feedback either.
I am also working on building a couple new preamps - one completely of my own design and another that is based on the Vacuum State RTP-3D - that don't use any negative feedback.
So they do exist.
Damping factor is a term used to describe how well an amplifier can handle varying reactive load impedance. This is generally not an issue for a preamp (unless, perhaps, it is also designed as a headphone amp). It's actually defined as the ratio of the load impedance to the amplifiers output impedance. Generally, the load impedance a preamp sees is fairly high (10K or more), so the damping factor will generally be a large value.