This hardy shrub would probably be much happier outdoors and may be deteriorating from being inside the house.

I agree, but it's probably a little late to take it out now unless you acclimate it very slowly. But, even taking it outside on days when it's not way too cold, might help some. Why/how did it end up in the basement instead of outside?

I bought it at the end of the fall and didnt put it in the ground. I tried overwintering some trees and shrubs outside last year and they didnt make it. That is why i put them in the basement.

The basement is probably not a good place to overwinter most trees and shrubs. If you buy things in the early fall, it should be fine to plant them out and let them start to establish before winter. In most cases, the roots will grow whenever the ground isn't frozen at root level.

If you buy containerized trees or shrubs in late fall, you could bury the containers in the ground or pile mulch around the outside of the containers and overwinter them outside. Even balled and burlapped or bare root plants might be OK if heeled in well, but personally, I would avoid this situation in your climate. The important thing is that trees and shrubs that are hardy in your area, need a period of cold to survive.

So will they be alright? I have been hardening them off, but only when it isn't too windy out. If I protect them from the wind I could probably put them out right?

What was the temperature in the basement?

The basement can be a satisfactory place to overwinter if the conditions are right.

Here in MN, Inkberry loses most of it's leaves during the winter. Perhaps I should say that our winter weather burns most of the leaves on the plant. Anyway, they grows new ones in the spring....usually. So there may still be hope assuming there isn't something wrong with the plant.

If it's been very gradually acclimated to outdoors, I would go ahead and move it there. One issue to consider though is the temperatures that the rootball will experience. I'm not sure what type of temperatures your area is likely to have through the remainder of the winter, but keep in mind that an unplanted tree or shrub is more susceptible to cold temperatures because the root system cannot deal with temperatures as cold as the upper part of the plant can. Heeling the pot into the ground or surrounding it with some type of insulation/mulch could solve this problem.

So far as whether your plant will make it, that's anyone's guess at this point. Without more information, we don't know its true current condition or definitely what's causing it to loose foliage. Giving it proper climate conditions and making sure it gets proper watering will hopefully help.