Thanks everyone for the input. I sprayed them both with Murphys Oil soap diluted with water - hope that was the right thing to do. My county extension service said the treatment for mites was to spray with "horticultural soap," which I could buy at Lowe's or make my own. So I used Murphy's since I had read about others' using it. I have nothing to lose since they are quickly on their way out. I thought mites was a problem that the west coast/dry climates had to deal with and that it was not an issue in an extremely humid environment! Well, we'll see what happens. If I can salvage just one of them I will be happy. Oh, I think I could see the tiniest of specks on the undersides of leaves which came off when sprayed. If they were mites, they were really hard to see (didn't have a strong magnifying glass). And I see webs all the time, but thought thay was just spiders since they're everywhere. (I still wonder if there will be a worm in the tomato when I cut it open!) :-)

Though I am not the OP, this has been a useful thread, thanks. I have a set of rubberwood folding chairs in natural finish that have held up very well, even though they have had rough use in the kids rooms. The bashed up finishes I mentioned earlier have all been on dark finished pieces. So I think that rubberwood might be good enough for many uses, but avoid those dark finishes. I searched on these forums because I wanted a new dining set. I was concerned about spending a lot and not getting good quality, partly from seeing the aforementioned bashed up pieces, and because we have a Scandinavian Design teak dining table with problems. This table had the veneer blister on the top about a year after purchase. It blistered and parts peeled off right at the middle where the integral leaf folds out. Underneath is clearly particleboard. It is unsightly and could never be repaired. We have been living with this for over 20 years but it has always been annoying. I always have to position a table runner over it. I did not want to have a similar experience with a new, much more costly table. I am looking for a traditional set because I have family antiques in the same room. I have seen now many online sites with dining sets that look intricately carved. I assume those are all made in China and are rubberwood or some other mystery wood; and may not hold up. I am afraid to order anything like this without seeing it in person. Unless I can find a local dealer and can actually see them, I am going to stay away. I have shopped now at several name brand furniture stores, and for the style I like the prices are well over what I have budgeted for this purchase. I am grateful this forum exists to do research before purchasing. Homework may take time but it is much cheaper than disappointment.

It looks like an asparagus fern (which is really a member of the Lily family). If there's no other plant nearby that could be dropping sap onto the 'leaves' then - well, I'd be suspicious and get some just-warm water and a paper towel and sponge it off. I'd be looking for small creatures along the stems or under the leaves, too. Quickest remedy is - squish. I'd also ease up on the watering over winter.

Just not ready yet. Still dig, divide, and replant in the fall - they'll get bigger next year if grown in the right conditions.