I once worked for an employee leasing company so let's make sure we are all talking the same language.
1. Temping Agencies- Employees on demand, hire for a day, week or month. call them and say you don't need them and your obligation ends.
2. Payroll Services- from self service to full service it's basically software that you pay to use. It helps you with all the paperwork of running your business. Many of ADP's services fall into this category
3. Staff leasing or People leasing- This is what the original poster was asking about. You still interview, hire and fire people normally. They usually provide you payroll services but most importantly the bundle benefits like health, 401k and Workers Comp insurance. They are considered "co-employees" if you don't need someone anymore you still fire them, they are without a job. But you can get breaks on some of the pricing of above benefits.
Staff leasing companies became really attractive because of the workers comp issue mentioned above but most of that has came to an end. Comp companies that many "high risk" employers were hiding inside these staff leasing companies and quit selling insurance to the staff leasing companies, putting them out of business.
While at one time they could save you money, for the most part in today's environment your biggest benefit is outsourcing the "hassle". It's like the small biz gets a big HR department. Any "comp" savings you get usually goes away.