This appears to be a cheaply (or carelessly) manufactured part. I do not think the cable jacket has broken or "split" according to the photo. I do think there is a visible gap because the cable jacket has pulled free of the utility box's wire guide strain relief. This can happen for a few different reasons.
- The jacket for the wire has been trimmed too short for the plug during manufacture. It does not have enough length when inserted and connected to the plug leads and has worked its way free from the plug during use very soon after you start to use it.
- Same effect as above but the jacket has exposed conductors because it has shrunk over some time because it is of a different material. It could be softer for abrasion resistance for example. It may continue to shrink as it ages.
If the cable is relatively new (you can still smell the plastic), the wire jacket is still relatively flexible. It can be stretched to close the gap enough to reinsert it into the wire guide (hole) of the cable's molded stress relief.
Starting at the opposite end of the wire, pull along the length of the wire to stretch the jacket. Apply a light tension several times until you see the gap start to close. Continue this until there is enough of the jacket to touch the plug. Work the loose ends into the stress relief so that the gap is closed. Continue to stretch the wire to get enough of the jacket into the molded plug to hold well. Use some cyanoacrylate glue (Krazy™ or Super™) to seal the joint between the jacket and the plug. Let cure COMPLETELY before you move it.
Notes: There are different kinds of cyanoacrylate for different materials and applications. Read the labels and get some advice from the hardware store owner on what's what.
When you stretch the jacket, the desired effect is not to pull the cable jacket free from the plug at the far end of the cable. Before you start, glue the far end of the plug and jacket at the joint to ensure it does not pull free from its molded connector. I found it helps to bend the far end into a tight "U" shape to help stabilize the relative position of the jacket and conductors inside. Increase the pressure as you pull along the cable toward the gap to prevent pulling the good end of the cable free. You may want to start halfway along the cable to see how it goes.