The fact that they are easily damaged makes me want to change my answer... A melon and a gourd would be able to make it in fairly difficult circumstances laying out on the ground. I don't bother to trellis any of the gourds (except luffa) because they are so heavy. I give them a pretty big patch together and let them do what they want. It's not ideal for picking or prettiness, but the patches produce and live well enough. But, cucumbers are another matter... unless they are one of those types that grow in bush form (which yours plant is not) they need trellising and care to get them thriving well enough to form mature cucumbers. Also, someone mentioned acorn squash... which might be a possiblity... maybe like a squash hybrid. I had some hybrids volunteer this year and they came in in some off the wall shapes that never matured and would just fall of the stem. I would suggest that if your plant does die, pull the whatever it is from the vine and do an autopsy of it. I'm pretty sure that we could help you identify it a little better by the size/shape of the seeds and color/spongy appearance of the flesh.