This could be an example of "grafting " it is rare but it can happen . It is usually in more closely related plant like pears on an apple tree; but a lemon was grown on an apple tree once . This is the first squash pepper grafting that I have heard of . Next time take a picture ; and by all means save the seeds from the pepper to plant next season .
What happened was the stems of the 2 plants came into contact and grew around each other . Then the stronger plant started feeding sap into the weaker one making the pepper a parasite on the host squash plant so the pepper no longer needed its roots .

FF,

I was thinking space aliens and crop circles, (grin) but your explanation is probably better.

ZM

I like both FarmFreedom AND zenman's explanations. I would've saved the seeds but unfortunately we just ate the thing. Maybe next time!

Taxonomically this can't happen. Really. Could a wasp lung system be transplanted or graft to a that of a whale? This is about the same. Pretty far fetched. It seems like a fairy story, probably is. I would love to hear someone refute this! I am willing to learn.
Hortster

They graft tomatoes tops onto potato roots . To give you inferior potatoes and tomatoes. You can graft giant fruit trees onto dwarf root stock to get dwarf fruit trees so it might be possible . The key here is that the pepper tasted different less hot . Unrelated plants have been grafted . so it is possible. The pepper would just get its sap from the squash in this case .

My point is this:
Tomatoes and potatoes are closely related taxonomically. Tomatoes are: Family: Solanaceae, Genus: Solanum, Species: lycoersicum; Potatoes are: Family: Solanaceae, Genus: Solanum, Species: tuberosum. Peppers and squash have no taxonomic relationship other than that both are in the plant kingdom. I would love to have someone tell me how this can happen without lab-produced GMO's.
Hortster

I'm late getting back to the naysayers. (Been in the VA Hospital). All I can say is that what happened, happened. I don't need to make things up. It's a strange hybrid, I agree and I really do wish we had saved some seeds. Will try again and see what happens. Thanks for all your good interest.

I agree with HORTSTER

Grafting (stem to stem) requires that plants are compatible and of the same family. Even then it is not that easy.

second, if this type of grafting ever takes place , between a yellow squash and habanero pepper, there woulh be two cases:

1- habanero top growing on squash stem/root
2- squash top growing on habanero stem/root

other case would be they become grafted in the root, underground. That makes a nice sci-fic story (LOL)

Then explain how a human can get a liver transplant from a pig ?