non-managed care plans are called indemnity plans. These are health plans that don't have provider networks, and simply reimburse a portion of your charges for any covered medical service. Indemnity plans have fallen out of favor over the last few decades and are very rare (less than 1 percent of US employees with employer-sponsored health insurance had indemnity plans in 2017). Dental indemnity plans are still fairly common, but virtually all commercial major medical plans utilize managed care.
