In my opinion as a project manager (other project managers may have other opinions), a risk can be ignored when its risk score is very low. In other words, its impact and its chances of occurrence are almost negligible.
Ignored risks should preferably be listed in the risk management plan, but their status should be ignored, and no contingency plans should be developed to mitigate these risks. Some project managers don't bother including ignored risks in the RMP at all.
Now let me give you an example of an ignored risk. You're working on an IT project in Nevada, there is a very slight risk that there will be heavy rain during the summer time (when the project is executed), and even if this happens then the impact will be very low because people can work from home. This risk can be ignored. (of course, there are better examples but this is what I had in mind).