The purpose of an underbust stay is to ensure a closer fit of the bodice in a strapless dress. It provides additional support to the underwires and creates a cage effect with the vertical boning. Just note how the boning extends over bust points across underwire - this can tend to move away from the body where the underwire is placed. This is, by the way, another reason why spiral steel boning is better than rigilene for example, which is less flexible.
I can imagine this dress had a waist stay as well, but was removed at some point. All in all, quite an interesting construction we are seeing here.
Happy Easter to those who celebrate, and a wonderful sunny weekend to those who don't :)
P.S.: Thanks a million for your amazing feedback on my patternmaking and fit series. It means a lot to me!