For a 'dead hang' the elbows are 'locked out.' Just as they are in an 'active hang.'
Some people are for some reason concerned about locking their joints out but it's perfectly safe. You have to do it in powerlifting and olympic lifting for the lifts to count.
The only main consideration is that there is a difference between straight locked out and hyper-extended locked out. Some people naturally present hyper-extended and this may not be ideal. Look up the Beighton Laxity Test, the ability to hyper extend the elbow (or knee) is an indication of joint laxity.
Everyone should have some range of motion beyond 180º (maybe max 10-15º at the knee, less in the elbow) but excessive range is the concern.
You can still carry active muscle tension while the elbow is locked out if you want, but you want to consider where that tension is.
It's important to remember that in this context, the dead hang is more of a stretch as compared to an active hang. So while you can keep some muscle tension (your grip obviously has to maintain tension) the arguable benefit of the dead hang is the space it frees up in the shoulder. Meaning you want to feel a stretch. You don't want the muscles you're trying to stretch to be too active (unless you are using a PNF stretching strategy perhaps), or they won't stretch. However, some supportive muscles like the upper traps, levator scapulae or serratus anterior (they won't be stretched in this position) could be active to provide support. In addition to actively elevating and upwardly rotating the shoulder.
I've seen this idea online quite a bit as a cure all to shoulder issues, but it really only works for specific issues. For instance, it's possible your issue isn't space, it's timing. Or your shoulder is already lifting too far off your rib cage. There are plenty of other things to consider when it comes to shoulder health. Certainly no harm in experimenting with it though, see if it works for you.