Remove the shoe with the lost casing from your foot.
Feel along the outside of the casing to find where the end of the drawstring is located.
Pinch the end of the drawstring to hold it in place so it does not retreat further into the casing.
Scrunch up the empty area of the shoe casing to try and minimize the space between the hole at the front where the drawstring should protrude and the point where the end of the casing is. This is easier with a soft ballet slipper than with a pointe shoe, since the pointe shoe has a firmer sole and toe, however, it can still be helpful.
Push the opposite end of the drawstring -- the end that is not lost and is still protruding from the hole in the casing -- into the shoe casing. Do not push it so far that it becomes lost, however. Use your fingers to feel where the drawstring bunches up inside the casing as you push the opposite end and try to straighten it out. This causes the lost end to move closer to its own hole, which can lead to retrieving the drawstring or make it easier for other techniques to retrieve it.
Insert a pair of thin tweezers into the casing hole where the drawstring should protrude and try to clamp them around the end of the drawstring. Pull the drawstring out once clamped down on it.
Insert a pin into the casing if the tweezers are too thick to reach the drawstring. A sewing needle is best but a safety pin can work as well. Use the fingers pinching the end of the drawstring through the casing to try and guide the end of the drawstring onto the point of the pin. Slowly pull the drawstring out once you have speared it with the pin.