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This could be crown rot. These articles may help:

http://www.gardeningknowhow.com/ornamental/flowers/plumeria/

http://www.gardeningknowhow.com/plant-problems/disease/crown-rot-disease.htm

It is best to just leave them alone and see if they start growing on their own again. The exception is that if there are an rotten parts, you should cut them off plus another inch or so. Wait to fertilize until you see new growth emerging. If they haven't put out any growth in another month or so, then you can cut them back.

Unfortunately I this looks like an infestation. It appears to be that the stalks of the plumeria have small holes oozing a black substance. This is a sign of longhorn borer infestation, and infected limbs should be cut off the tree and burned immediately. Although the holes may not be actively oozing in the dormant season, cut away any bent and shriveled limbs with these holes at the base during winter pruning.

They will, actually, need a more even ratio of NPK values to thrive. They prefer acidic soil, so adding too much phosphorus will raise the pH of the soil to unsafe levels for the tree. The nitrogen will help keep the pH down to a more acceptable level.

This article will give you more information: https://www.gardeningknowhow.com/ornamental/flowers/plumeria/growing-plumeria.htm

This is a severe fungal infection. I would correct immediately with wettable sulfur and dolomitic lime. It seems very advanced, so there is a chance that it will be lost regardless of being treated. Sometimes things like this are unavoidable unless they are caught at the very first sign of infection.

Try this treatment, as it works very well, but like I mentioned... This is very aggressive, and there is a chance that it could be lost.

This is not, usually, fatal. It can indicate that the plant is not receiving enough light, or may need a bigger container.

This article will help with the care of these: https://www.gardeningknowhow.com/ornamental/flowers/plumeria/growing-plumeria.htm