Yes, this is why many organizations like to issue a 1099 even for low paid workers. They save the unemployment insurance cost, the worker's compensation insurance premium, and the matching employment taxes for social security and medicare. The legal way to do that is to hire people through an employee leasing firm who provides these benefits to the worker. That is why you pay a premium over the hourly wage the worker receives. It covers those costs as well as a profit for the leasing company.
Taking a worker who you are paying and compelling them to sign an agreement in order to keep their job will not likely change anything. There is no one single factor that determines a worker's status. You should review http://www.irs.gov/businesses/small/...=99921,00.html before making any final decisions.
Workers deserve to be covered under unemployment insurance if they are in fact employees, because the law provides this benefit for them. They also deserve insurance if they are injured on the job for the same reason. Denying them these benefits to save money for the employer is abusive to people who already don't make much money and have few options but to endure what ever is imposed upon them.

