I assume that it's still in/been in flower recently, in which case a gentle support would help with appearance until flowering is over & it can be cut back for over the winter. This 'flopping open' is common with sedums especially if they've been 'well fed' or are a large mature plant.
The dead stems from the previous years growth need carefully cutting out once flowering is over. If this is done late winter/early next spring you can often see the emerging signs of the new growth for next season, so take care not to damage those.
I've discovered that doing the 'Chelsea Chop', ie reducing the height of all shoots by about half during late May (Chelsea show week a good reminder) helps eliminate the need for any staking & no flopping. It means that the plant produces shorter, sturdier flowering shoots that possibly flower a wee bit later, but not a problem to me. J.
Thanks for a fantastic answer, jo4eyes.
I have a clear plan of action now!
Although, it has raised one or two additional questions in my mind. Firstly, will the shoots currently flowering die after flowering? If so, when should they be cut back for best results?
Many thanks again for your comprehensive answer!