How do I repair this rot/insect damage on my wall plate?

I am removing the lath and plaster (to add insulation) in my 1929 bungalow that I just bought in Portland, Oregon.

Along an exterior wall, the last piece of lath and a little bit of the plate were mostly wood powder.

I scraped away about 1/4 – 1/2 inch of the soft stuff around the corner of the the plate, after that it's solid. The studs also appear to be solid.

My question is, what is this, dry rot? Insect damage?

And what do I do with it? Should I replace this section of the plate? Spray some kind of anti-fungal agent on it? Leave it alone?

If it matters, the house was empty for at least a year (maybe two) before I bought it.

Update: I've found this in another room too, in a corner. My best guess is that it simply was dry rot, caused by moisture trapped in the corners. The moisture, I think, was left over from the original plastering of the walls. What I didn't show were large blobs of plaster that had fell behind the lath, and dried on top of the rotted area, getting trapped in the wall. I could be wrong, but everything left is solid and dry, so I assume the rot died a very long time ago.