Hi. It is a little tough to know what is going on without a photo, but the odds are good that you aren’t dealing with anything particularly serious. This page on Ilex glabra (inkberry holly) from North Carolina State lists relatively few common problems that fit your description. It says that leaf spot is an occasional problem, so that could be the issue. This page on inkberry from Ohio State also describes leaf spot as an occasional problem. I could not find any information specifically on leaf spot in inkberry; pages like this one from the U. of Massachusettes focus on other hollies such as American holly (Ilex opaca). It notes that leaf spot doesn’t usually cause significant damage, and it only recommends sanitation as a possible way to reduce infection (i.e., cleaning up old leaf debris). It is also important to keep in mind that even though hollies are broadleaf “evergreens”, they do not keep their leaves forever; they are typically replaced each spring, at which time the old leaves fall off. Some of what you are seeing could be normal leaf turnover. Additionally, one well-known liability of inkberry hollies is that they tend to lose their lower leaves and become “leggy”, so this could also be what you are seeing. If shrubs are still producing plenty of new leaves that look normal, that is an indication that their overall health is pretty good.

Hi. Unless you have a compelling reason to cut them down, I would at least wait to see what happens. I would be extremely surprised if it were something that were going to affect other plants, so you are at little/no risk in letting them be and seeing the result. If you think it is something more serious, photos would help a lot in terms of figuring out the issue.