Everyone who does laundry should have a bodkin. It looks like a pair of tweezers with a small ring on one end.
Then your drawstring will be back in position.
Save the bodkin for use another time. Sometimes, you can use a safety pin to do the same thing, but attaching the safety pin and using it to guide the string through the area. The reason the bodkin is better is because it is narrow and some eyelets are too small to allow a safety pin through it.
Bodkins are very inexpensive and can be found in the sewing section of department stores, fabric stores and craft stores. Amazon even sells them for under $4.