• The leaves look like a firespike; are the stems stalk-like?
  

The stems are very thin and in a dense clump but are woody and upright. It almost looks to me like a shrub that has been cut back hard, but this is a new house so I don't know the history of the plant. It does resemble firespike, but I can't see how that plant could have survived last year's Northeast winter.

Here is a picture of the plant in early spring before leafing out (in the foreground). Anyone have a guess?

That's a weird habit. Almost looks like a witches broom growth. Can you show a close up of a stem from the side so we can see the branching form?

Here are a few close ups--two from the sides and one from the top.

I also have what I think may be the same plant growing in a bed of pachysandra. Compare especially the purplish new growth to the top of the mystery shrub in the photo directly above. I had assumed the one below was a tree seedling, and I was going to pull it.

That last picture looks like an ash seedling - Green or White Ash, if it was around here. Ash leaves are compound but a root sprout/seedling like that often has un-typical leaves. And I see your 'witches broom' type plant is growing right next to and old stump, so it might just be making water sprouts from the roots.

Agree last picture looks like Ash.

Could the stump have been dosed with herbicide which might produce those weird sprouts? They definitely look distorted and unnatural.

Now this has me interested, so I'll dig down a bit when I get home and see if I can see whether the weird plants are connected to the stump. I suppose it's possible that herbicide was applied to the stump, but I don't know the history. The photo I posted without leaves is from April 2014 when we were doing the home inspection, so the plant has gone through at least one full season of growth in that form during 2014. The stump doesn't look fresh but it's also not in a state of decomposition yet.

Do you all agree that the plant that looks like an ash seedling and the weird bush might be the same plant? The veining on the large leaves is similar, as is the lime green color, and the three leaflets of purple-colored new growth also looks similar.

Well the twigs on the weird one could be ash twigs but unless the distortion has been extremely radical the foliage bears little resemblance. The ash is pinnate and not toothed whereas your oddball does not appear to be pinnate and is quite jagged. However, I wouldn't rule it out.

I agree that it's ash (Fraxinus)

So I dug down a little bit and the base "stem" for the oddball shrub does seem to connect back to the stump. If you google epicormic growth on ash, there are images of stunted, shrub-like growth that looks somewhat similar in form to what I have. Apparently this usually results "in the wild" from a tree being stressed by disease or emerald ash borer, but maybe stress from cutting it down entirely could cause the root system to send this growth up. This is a working theory but interested to hear anyone else's thoughts. In any case, I think I'll let it be for the time being.