Hello all, I have scoured the internet in search of information on this plant. I acquired it several years ago from someone selling off their plants, and it has really done nicely. Now, I'm thinking of making cuttings, and I'm not sure what it is! My research:
1. At first I thought it was a euphorbia cristata, not grafted but somehow rooted. I thought the stubby stalks eventually changed into the coral like part. Then I read, no those are the original graft trying to grow back, remove them....however, it does not appear to be grafted.
2. Every now and then it produces a flower. When looking online it appears to look just like stapelia variegata, in the carrion flower family. The stubby stalks look right, but not the coral like part.
3. It is so close to the ground level of the pot I can see if it's one plant, but "to me" one of the stems of the coral like part looks like a stubby part that's twisted as it grew.

I give this plant almost zero attention and it thrives. BTW I live in Ecuador. Anyone have any ideas? Photos attached for reference.

The pretty bloom is Ceropegia mixta or by its old name Orbea variegata! I think what you call coral might be the cristated form of the same plant.
Starfish Cactus (Ceropegia mixta)

Thank you for the information! All of the photos online of that type plant seem to only feature the 'stubby stalks' part with flower. I have yet to see one with a cristated (thanks for the word ) portion. It makes things very confusing. Thanks again!

to the forum!

I believe Ursula has hit the nail on the head. The flower is the best identifying feature.

Some notes on wording (since I live in Mexico, also a Spanish speaking country)...

English - crest (n.), crested (adj.)
Spanish - cresta, crestado/a
Latin - crista, cristatus/a

The much more common ending is the fem. one (-a) since the words for plant and form in Spanish and Latin are feminine.

I see you live in Ecuador! How wonderful is that!