Not sure if its a ios 10 bug or my iphone 7 but when I switch the toggle to silent when someone calls me it still rings?
Have u checked the do not disturb in settings to see what it might be set to? Did u try to power off the device and start it again?
Is is a contact on your contact list? If so check your contact under ringtones and make sure emergency bypass is off. If it's on it will still ring even when phone is silent