Essexella fossils date back to the Carboniferous period, when northern parts of Illinois hovered just above the equator. A local river delta fed into the sea, creating a network of brackish wetlands home to sea scorpions, centipedes and early amphibians. Many of these creatures were buried by mudslides, which protected their remains from scavengers and decay. In the 19th century, coal miners began excavating an area, known as Mazon Creek, for fuel, and the fossils turned up in their spoil heaps.

Collectors have been finding the remains of these critters in the Mazon Creek fossil beds for more than a century. Most of the fossils are entombed in ironstone nodules. Cracking these concretions reveals the imprints of soft-bodied animals that resemble bulge-eyed aliens. In the 1950s, a local collector named Francis Tully discovered the imprint of a torpedo-shaped creature with a nozzlelike mouth. The taxonomic identity of the “Tully monster” has perplexed researchers ever since.

Essexella was similarly perplexing. Nondescript fossils turned up by the thousands at Mazon Creek, and they were often sold at local flea markets, or even discarded.

Scientists published the first detailed scientific description of the blobs in 1979. Essexella fossils are composed of two structures — a textured, barrel-shaped region and a smooth bulb. Researchers posited that the textured area represented a skirtlike curtain that wrapped around jellyfish tentacles. The rounded region was the jellyfish bell.

But as time passed, this description struck many researchers as odd.

“We were really shoehorning it to fit the jellyfish model,” Dr. Plotnick said.

No living jellyfish have curtains around their tentacles. Such a curtain would make swimming and feeding cumbersome. The uniform shape of the blob fossils also perplexed Dr. Plotnick. “If it was a jellyfish that fell on the seafloor, it would just splatter out in all directions like an old string mop on the floor,” he said.

Dr. Plotnick tested some other hypotheses to explain the blobs — such as gelatinous, barrel-shaped critters called salps or colonial congregations of tiny creatures known as siphonophores — but each new identity failed to explain Essexella’s anomalous anatomy.

In late 2016, Dr. Plotnick and a colleague, James Hagadorn, a geologist at the Denver Museum of Nature and Science, investigated the motherlode of blobs. They were at the Field Museum in Chicago, a repository for Mazon Creek fossils that has the world’s largest Essexella collection. Most had been donated by amateur collectors who were too intrigued to leave the fossils in the scrap heap.

The scientists sifted through drawer after drawer of the splotchy specimens. They lined up several fossils to photograph and compare side by side on a table. One of the blobs caught Dr. Plotnick’s eye. As he rotated the fossil upside down, he was struck by the clarity that the change of perspective offered.

“It looked like the bottom of an anemone,” Dr. Plotnick said. He added, “That was one of only a few times I’ve actually had the classic eureka moment.”

As Dr. Plotnick brushed up on sea anemone anatomy, the ambiguous blobs came into focus. “All the things that bothered us about this being a jellyfish now makes sense,” he said.

Instead of being a jellyfish’s bell, the rounded region of the Essexella was an anemone’s burrowing base. The textured barrel was not a tentacle-enclosing curtain but the body of the anemone. Some specimens are preserved so well that the scientists could see the muscles that the anemone used to bend and contract.

Dr. Plotnick, Dr. Hagadorn and their team redescribed Essexella as an ancient anemone last year in the journal Papers in Palaeontology. Because of their soft bodies, ancient anemone species are mostly known from only a handful of poorly preserved fossils. With thousands of relatively well-preserved Essexella specimens, this once puzzling species is now the best-known anemone in the fossil record. Dr. Plotnick posits that these animals once lined the floor of the Mazon Creek estuary.

This isn’t the only time that paleontologists have flipped the scientific script to clarify the identity of a bizarre fossil. Reconstructing any ancient animal is tricky. After millions of years in the ground, fossils have been warped and weathered, crushed and scattered and stamped flat onto slabs of stone.

Sometimes, a fossil’s preservation alone is enough to disorient researchers. For decades, paleontologists were stumped by why armor-clad dinosaurs called Ankylosaurs were almost always fossilized upside down. In 2018, a team posited that the heavily armored animals often went belly up because of bloating as their carcasses floated out to sea.

And then there are the evolutionary oddballs that are difficult to decipher no matter the orientation of their fossils. In 1869, the paleontologist Edward Drinker Cope mistakenly placed the skull of an Elasmosaurus, a marine reptile, at the end of the creature’s tail instead of its elongated neck. Othniel Charles Marsh, another paleontologist, seized on Cope’s error, igniting a rivalry that would fester into the so-called Bone War.

Even weirder was Hallucigenia. For decades, researchers could not make heads or tails of the creature, a worm covered in tentacles and stiltlike spines. Then they realized that its head was really its tail, and vice versa. “That was fun and not a mere detail,” said Jean-Bernard Caron, who is a paleontologist at the Royal Ontario Museum and a co-author of a study in 2015 that determined a bulb on one end of the Hallucigenia was the creature’s head. Better-preserved fossils of a related animal in China also revealed that Hallucigenia, like Essexella, was originally reconstructed upside down.

“Clearly Hallucigenia has seen many flips,” Dr. Caron said.

While Dr. Caron’s work helped straighten out Hallucigenia, a recent paper upends his 2012 description of Pikaia, an enigmatic wormlike creature from the Burgess Shale in Canada that was purported to be an early forerunner to vertebrates. The new study suggests that a mysterious tubelike organ that researchers thought ran along Pikaia’s back (and may have been an early nerve cord) is actually the animal’s gut cavity, running along its belly.

“The animal is now on its head!” Dr. Caron said. Yet another fossilized creature got a new story when it turned over.