How would someone go about accomplishing this goal?
How to sew a straight stitch for mending a pillowcase seam by hand?
Thread the needle using a wire threader, to save many minutes. Once the thread is through, double it back for strength, tie a knot at the end, leaving the thread twice as long as the pillow case. That way you won't have to stop in the middle and thread a new needle. Turn the pillow case inside out, and begin at the edge closest to you. Pierce the fabric, sending the needle away from you, and bring it back out 1/8th of an inch further, in and out, each time. Repeat until the entire edge has been re-seamed. Tie a knot at the end of the pillowcase so it won't unravel in your sleep. Turn the pillow case right side out, and voila your seam will be repaired.