If the provider is contracted with the insurance company, the full amount owed after the insurance has paid its portion must be collected.
Let's assume your provider participates with Acme Insurance, charges $100 for XYZ procedure and Acme Insurance reimburses that at $78. Your provider must collect the full $78. So, if the patient's deductible hasn't been met, the provider must collect $78. If the copay is $30 and the insurance paid $48, the provider must collect the full $30. If the patient's coinsurance amount is 20%, the provider must collect $15.60. The only way that this can be adjusted is if the patient demonstrates financial need according to the provider's policy and procedure. Whatever formula is used to determine financial need must be documented and it must be applied equally no matter who is the patient.
If your provider is not contracted with the insurance company, then the rules are a bit different. In these cases, it is OK to balance bill the patient for the difference between the "usual and customary" reimbursement rate and the provider's charge. In cases like this, I know of no rules (unless something is specific to your state) that would prevent the provider from legally collecting less.
Hope this helps!