Hey y’all, first time posting.
I have an old alder that I recently became the caretaker of, and it was really sick when I got it last month.
It had dried out and the subtrunks and whole side have died off, leaving only 4 branches on it.
It’s bouncing back rapidly.
I was just wondering if anyone had any idea if it was safe for me to delicately remove the subtrunks and some of the dead bits?
How traumatic will the work be? Lots of tugging and tearing or carving? If so, you will put a lot of stress on the roots and on a sick tree, I might just wait until it’s a healthier tree. The deadwood isn’t going anywhere 
Are you in the northern hemisphere? If so your tree should be outside or in a cold shelter and dormant. I would aim for a gentle repot at the first suitable moment late winter early spring when the tree is leaving dormancy (buds start to push). If you are in the Northern hemisphere protect the tree from frost and balance water and oxygen. Only water when the soils starts to dry. Be aware that this should not only be surface dry but the core should have lost moisture but not bonedry.