I recently saw a couple of dickies from the dark ages and I was reminded that sometimes we need to change the look of our clothing. A top that is cut too low can reveal too much, including crepely skin and sagging girls. So instead of a dickie the TV sales shows are hawking inserts to cover the deep V and act as a camisole. There are also camisole bras available. However, I would like to offer an alternative. If you have a pretty scarf, you can place it inside the neckline of a dropping top. Of course this would only include relatively small scarves unless you want to emphasize a large front.
If, however, you have a scarf which is pulled, or otherwise damaged, you could cut it into a deep triangle large enough to stretch between your bra straps in front and with a little left over on the sides. Hem the piece all the way around, either by hand or on a sewing machine. Then pin the scarf under the bra straps and voila there is a dickie. And you made it.