You may keep them unless they are spotted from mites or leaf spot diseases. If your Cordyline is growing at an indistinguishable rate it will take longer for the plant to suck all the nutrients out of the browned leaves before dropping them naturally. Probably by now ( 9 months after your post) you can trim them off if they are the lower older leaves. Just know if you change anything about their culture they might bounce back to a deep maroon/brown green if they are lower leaves. A shocked cordyline will neglect to nurish 2/3 of lower leaves turning them an unattractive color but possibly without dropping them. If they are papery like papyrus then they are long dead and removing them is fine. Heck removing lower cordy leaves is always fine I'd just add a bit of nutrient solution to the next water bath and give them brighter shade for a few days. Remember low humidity will brown leaf edges working its way into the center. None of this applies if they are new leaves. I hope to see an update on how the color is now. I'm suspicious that the first post is actually 'kiwi' or 'pete's rainbow". Let me know if I didn't make sense or miscommunicated. My miss Andrea needs a humidifier and to be cool but my red sister doesn't and likes warmth. Hope that helps. I'm z7a in Nashville and all my Cordylines are indoor specimens that enjoy co-potting with tropical epiphytic vines for humidity and awkward small talk.

The blue is not fungus, its residue from fungicide thats been used before you bought the plant. Many fungicides leave a blue or white powdery residue. Nothing to worry about other than that it's toxic if it gets ingested, licked by cats.... In production they keep them very humid and will use fungicides to keep the leaves in pristine shape for sale as the tips often go brown. They should use a mild detergent to clean them for sale. Cordylines also often shed lower leaves when placed in a new environment especially a much drier one. This is also not something to worry about, though you could improve humidity one way or the other. Look at the roots if they are nice and white thus healthy it's not a root problem. Root or stem rot will cause the lower leaves to drop off very quickly. It's unlikely this is your problem indoors though. Older leaves will look spotty and brown parched, before they abort, also no problem. However the large "water mark" in the healthy pink leaf is symptomatic of something, probably dry air in your case or possibly over watering, no drainage at the roots, or even lack of water at the roots, check all these things. It could also be burnt from being too close to a window or a lamp. To increase humidity sit the pot on some pebbles in water don't over water instead. They do like a moist soil but not a boggy one. Indoors they also want the brightest light possible short of actual sun, certainly in summer as the leaves can scorch through glass. The leaves are thin in most cases and burn easily or dry out easily especially the new leaves. Also don't feed more than just a tiny amount once a year indoors. Cordylines quite frankly don't make the best house or office plants because they love humidity and warmth so much and because the leaves are most often quite thin. To recreate ideal conditions would make anyone using the room uncomfortably steamy. However if your climate is good you can place them outside for a few months (even just summer) then inside for one, rotating them as you go, or just inside for winter. Other wise look for the varieties with the thickest leaves to try, there are one or two that with some help should do better as a result. Off hand C. fruticosa "Vanuatu" is one, shiny largish jet black leaves, arranged beautifully. I've never had any problems with it's leaves outdoors in full sun and drenching rain, humidity and a dry warm winter. Some of the rounder paddle shaped small ones or the larger leaved reds with the same thick leathery leaves might also do. Dracaena are all round are far better than Cordyline fruticosa for permanent indoor use. You are unlikely anyway to get a fungus problem on the foliage indoors only possibly at the roots or the cane. Fungicide could help with that but then it must be mushy wet and black to be that. Lower older leaves don't always look their best indoors but it is technically better to wait for them to drop off rather than cutting them off or the plants stem (cane) might get thinner and thinner in the process, bending over and ultimately die. Hope they've survived meantime anyway!

if you can't determine just put it sideways and pile some moist long fiber sphagnum moss on it loosely. and enclose In transparent container. check ev week for buds: once the buds start you'll know which way is up, then you can plant it. laying it sideways is advantageous since it can develop several buds, so you can get a few stems going and much better looking plant.

Ciedyline is not an annual. I successfully overwintered mine for several years. After it “trunked,” I tried following the advice of dear Campanula, to score the trunk to stimulate growth lower down. It died soon after.