I coined the term "theoretical cryptid" to describe animals which haven't been sighted or scientifically recognized, but which have been proposed in order to explain some type of phenomena.
The most famous example of a theoretical cryptid is the bloop. It was an extremely loud underwater sound first recorded in 1997. Due to how loud it was, it was theorized an animal larger than any currently known one must've made it, though we now know it was likely ice breaking.
A famous example of a former theoretical cryptid would be the xanthopan. In 1862 Charles Darwin received an orchid with an extraordinarily long stem. He theorized that there must be a type of moth with a long proboscis that could pollinate it. 41 years later one was described.
Another popular example would be the paleodictyon, or whatever left the paleodictyon. Paleodictyon is a trace fossil, meaning a fossil that was left behind by animal activity but isn't actually of an animal, that's been found for over 50 million years.
Scientists have never been able to find what's making them. Some say they're burrows of worms or other animals. Other argue that they're not trace fossils at all, but rather the fossilized remains of a type of xenophyophorea. The DSV Alvin searched for them unsuccessfully.
Non-carbon based lifeforms have also been proposed. All known life on earth is structurally made up of the element carbon. But due to how different other planets are, some proposed that life on those planets could be made up of other elements like silicon.
In 1997 bite marks found on a dead narwhal were attributed to the cookiecutter shark. These marks were far larger than the cookiecutter's usual bites, as they only grow to 2ft (60cm) long. This led some to speculate than an unknown giant species of cookiecutter made them.
In 1939 strange footprints were found in New Zealand's Ruahine mountain range. These prints were described as a foot long, with a four inch and six inch twos on opposite sides of the print. A museum curator said they resembled a reptile's, but were too large for any known one.
An ancient example is the Triassic kraken, a squid hypothesized to have lived in the Triassic era. Due to how a group of icthyosaur fossils were found in a strange pattern, it was theorized in 2011 that an unknown 100 foot (30m) squid used them to make a sort of self portrait.
In the remote Kergulen Islands, explorer James Ross noticed odd horse-like prints on his way to Antarctica. He described them as recently left in the snow, despite no known horse species behind found on the island and no known shipwrecks nearby.
This is not an exhaustive list of theoretical cryptids, but hopefully this was enough to give you a basic concept of what a theoretical cryptid is.