I'm sorry I don't know the cause of your damage, but I have a lot of experience with sedums, and can reassure you that a healthy plant can grow even if the top is damaged, dead, or broken off; and even if the roots have come out of the soil and completely dried up.
I live in Massachusetts, growing zone 6, (-10°F, -23°C) and have a number of varieties of sedum, both upright and creeping. Some thrive in an area that gets up to 6 hours of sun a day, even at the height of the summer, but most do best in part shade or full shade, with a maximum of 4 hours of indirect sun. I frequently move them, but keep them in the same conditions, so I don't have the problem you're having.
There's an animal in my yard who rearranges mine. I regularly find them dug up, broken into pieces and scattered all over the place. Generally the top growth is dead or absent and the roots are dry and shriveled. If I ignore them and go back a few weeks later, there is already new growth. The pictures below are of a piece from a large plant that I found with no foliage growth at all on the lawn about two weeks ago. I threw it under the bird feeders. Today I found it in a different spot, lying sideways on top of the ground, with dead-looking roots and nice new growth!
Once you've figured out the problem, you may need to transplant it. If so, I've had success with just digging a hole and dropping it in, but when starting with a compromised plant, this is what I recommend to maximize chances for future growth:
Check for bugs or other damage to the root. If you find anything, gently scrape it away.
Dig a hole (or use a container with room for a hole) about twice the size of the root ball.
Partially fill with some loose soil. Some people use compost, but I generally just loosen up some garden soil until it's light and aerated. If you're using a container, I recommend a potting soil made for that purpose.
Set the plant into the fresh dirt, keeping the top of the root ball at ground level.
Water it well for the first few days, then switch to a regimen of waiting for the topsoil to dry out before watering again. In general, once, established, most sedums would rather be too dry than too wet.