Answers from Master Gardeners: • From my book: Handbook of Natural Insect and Disease Control, this sounds like squash vine borer. I did not know they also attached cucumbers. Without seeing the plant, it’s hard to figure out what happened. Perhaps in the course of transplanting, the soil may have fallen away from the roots and they didn’t get a good start in the ground. It is important to keep the root ball intact, plus make sure the plant is well watered at the time of transplanting. Since it happened about a week after the transplanting, it sounds like damping off disease. • This could be a cutworm problem. They will eat all the way through a stem or practically all the way through as soon as they can make it to the young transplants with tender stems. The solution is to put some physical barrier around the stem until it toughens: like a cardboard collar, a little cup with the bottom cut out, etc. The cutworm will bump into this barrier and go elsewhere.
I transplanted some healthy cucumber transplants. In a few days, the middle of the stems dried up no bigger than a string. Above and below the shrunken stem the plant looked healthy with diameter of the stems the size of a pencil. After a few days, tops of the plants suffered and died because no nourishment could get to the top. I raised the transplants from seeds in my greenhouse and they were healthy when I set them out with the onset of the problem appearing after five to eight days. What was the problem?