Somebody needs to attach images of this. I suspect that it is not a problem at all but, as Jean says, aerial root initials. A picture would solve the mystery in a nanosecond.

Amy, Plumeria are very hungry when they are actively growing and blooming. Some of my colleagues feed them every day with diluted fertilizer (about 1/4 strength). I fertilize at least weekly during the growing season. When they go dormant, they need very little water and no fertilizer. Here the humidity tends to be low, so the soil drys quickly and I have to water frequently. In your area, it won't be as necessary. Some prefer to let the soil dry to about 2" deep between waterings, some don't let it get that dry. What is critical is the ability of the soil to drain. Plumeria need fast draining soil. The faster the soil drains, the more frequently you need to water, and the more slowly, the less frequently. Plumeria don't like soggy soil, so don't let them sit in soggy soil. Some use MiracleGro, some use Spray N Grow with Bill's Perfect Fertilizer, but there are a lot of balanced fertilizers out there. I'm sure others here will let you know what works for them. Good Luck Mike

I want to underscore what ken_a said. Bite the bullet with that thing, right away. It is a junky tree, even when healthy. Research then choose a worthy tree. You an find out how much life it might have had in it as you chuck pieces of it into your fire pit. I know it can be hard to see a tree succumb, but in this case, it is a blessing. Treat yourself to a handsome tree. Pone thing you might be able to try is to take a long 1/4" drill bit and drill into the trunk a few feet up. There's a good chance that you'll only get brown looking crumbs coming back. Other things to consider: you wouldn't want that dead looking tree to topple over during a wind or ice storm and you'll be removing an eye sore. Near a local pond where we sail, there is a little house with several of these mostly dead Lombardy poplars near the roadside. They are too barren to offer any privacy (presumed original intention). Every time we visit that pond, I want to help the owner take the things down. Keep looking for a nice tree. You will be happy you did so.

sounds like scale to me too, they don't tend to live on the leaves, just the woody parts of the plant, neem oil ought to help