Cloverfield is a giant kaiju about 300 feet tall (about the size of the Statue of Liberty - give or take five feet) that originally came from the sea, it was awakened by a Japanese sea rig. It awoke only to come ashore in the United States, New York City. It caused widespread damage to the city throughout its "rampage". As the creature (itself despite its size) was a juvenile it wasn't in fact on a rampage, it was trying to get away. It was scared and frightened of the human forces that tried to destroy it and the new world. It tore the head off the Statue of Liberty and threw it onto the mainland, destroyed multiple buildings by simply walking past them and bumping them or using them to grip with.
Biology: its biology is quite unnatural, it's quadrapedal (using four legs to walk with but can stand upright for brief moments, greatly increasing its height) and has a tri-finned tail, and has an extra pair of appendages tucked in under its chest about what would seem stomach height, it has a very large head, with extremely big jaws, and weird-looking sacks behind the eyes that are thought to be natural breathing apparatus (for both air and sea water breathing) and the pupils in its eye are very large covering almost all of what's visible of the whole eye. It does have supposed feeding tubes on its underbelly, scenes where humans were pulled into this area were cut for unknown reasons.
Parasites: It has parasites that are about the size of a domestic dog. It sheds the parasites as a supposed post birthing ritual (despite the fact that the creature has been under the ocean for thousands of years) these parasites attack humans and infect them with some sort of quick acting virus. the infected host over time receives symptoms such as bleeding from the eyes, pale skin, sluggish movements and lightheadedness. ultimately their abdominal region will expand and swell causing a painful explosion and a very quick death. its unknown how many parasites fell from the monster. but they caused a lot of the casualties of human soldiers and claimed the life of one of the group members of survivors in the 2008 film.
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Death?: Yes. It was killed. The military bombed it despite its extremely durable skin. The United States issued a hammer down protocol from which the two remaining characters at the end were killed along with the monster itself. However, at the end of the film where the credits end, a garbled voice audio plays which if played in reverse says "it's still alive".