Fig Tree in Dire Need of Help

I pruned my 4-year old fig tree in early February. About 4 weeks later, I noticed two things:
1) all the remaining branches were hollow in the middle or with a white "blob" that feels like Styrofoam.
2) More distressing, there are many powdery "sprouts" along the branches and trunk. They are gray in color and dissolve into powder when I touch them. I've searched high and low online for an explanation and can't find any.
My tree was healthy before pruning. Now I'm not even sure it will make it or what I should do. There is no life showing from about 12" above the ground. There is one little green knob a few inches up from the bottom, and a new shoot coming up next to the trunk.
I have a photo but the website is having an error and won't let me post it. I'll try again later.
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If you do the fingernail test is there any part of the Fig trunk that is green?
If you scroll down on the image, you can see the little things that are sprouting out of the tree. It doesn't look like the cottony-cushion-scale. We can't see any evidence of bugs or eggs. Blair, there is some life further down the tree, about 12-inches or 1/3 meter from the base.
In answer to your first question, the stems are hollow and exude a sticky latex sap, Figs are closely related to india rubber Plants so this is normal.
These growths look almost like roots. Many species of fig tree produce aerial roots so perhaps yours is following an ancient genetic trait.
I have grown fig trees in pots for some years and find that they can sprout from a bud low down the stem if they are pruned hard back. It is a good idea to take cuttings so that you always have a couple of fig trees as spares, plus they fruit very well in the greenhouse if they are gown as a single stem and kept about 3 or 4 feet tall.
Figs are very greedy and can deplete the soil around the root area.
I think it's some kind of bug. When I brushes away the powerdery growths, there are tiny little holes. Some nasty insects have bored into my tree. I don't know if I can save it.
I think you have something rather nasty there. Where do you live?
http://www.walterreeves.com/insects-and-animals/asian-ambrosia-beetle-control/
If this is in the UK it should be notified to someone - DEFRA?
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
Ceres, you are right! This is exactly what I have going on. Thank you so much for solving this mystery for me. Dovefromabove, I live in the US in North Carolina, so no worries for you. I've been reading up on the ambrosia beetle and it has infested many trees in North Carolina and South Carolina. Apparently, my only course of action is to remove the tree or cut it flush to the ground and let it grow again. While I'm very disappointed that this is the outcome, it's good to know what's going on.
The good news is that figs will almost always come back after being cut to the ground.
Good to know. Bob. Thanks. Maybe we'll try that.