For many years, some people have thought that a coffin is not cremated with the body and is instead reused. This is not true because the coffin is always cremated with the body. This is for reasons of hygiene and dignity.
To remove a body from a coffin once at the crematorium would be a health and safety risk for the crematorium staff not only because of the weight involved but there may also be a risk of infection too. A deceased in a coffin is much easier to handle and place into a cremator.
More recently, a reusable decorative shell has become available which covers a very basic coffin (sometimes made of cardboard). The purpose of this is that the shell may be removed and reused. These are not yet popular probably because many may feel that their loved one deserved a proper coffin or possibly because the cost involved is not much cheaper than a simple wood coffin which is both presentable and dignified.