Yes. The study of insects and arthropods (centipedes, spiders etc) with regard to legal issues is called 'forensic entomology'. Arthropods that eat dead bodies are particularly important when solving crimes.
The order they arrive in and their natural life cycles allow the forensic entomologists to work out time scales. If you have a strong stomach, read on.
A dead body starts to smell which attracts insects. The first ones on the scene are the Diptera, particularly the blow flies (Calliphoridae), and the flesh flies (Sarcophagidae). Female flies lay eggs on the body, especially near orifices and in wounds. Flesh flies deposit larvae.
A day later, eggs hatch into larvae, which eat the dead tissue. The grow quickly and moult twice within four or five days. When fully grown, the larvae start to move around more. They moult into pupae at around 18 to 24 days after the eggs were laid. It varies according to the species and the temperature in the surroundings.
There are many other creatures which come along when the bones are exposed, for example, and some insects live in very decayed bodies.