As you have read here, a DNR and a living will are 2 different things, in most places.
A DNR is something you decide or your family decides. Usually after your health as been declining for a while. Or if you are in the hopsital with a catastrophic event. For example, you are in the hospital with the flu, and you get septic, then you have a cardiac arrest. During the cardiac arrest, you have horrible brain damage. Then you are in a coma, septic and have mutli-system organ failure. They run tests, such as MRI's and EEG's, and see the pt (I will stop saying you) has no chance of recovering brain function. Then the family may opt to chose a DNR order for this pt. That does not mean they wll immediatley withdraw support. Only that is another cardiac arrest happens, they will let the pt "go."
Now, say this pt recovers from the organ failure but not the brain damage. The pt is then able to be transferred to a nursing home, with a feeding tube,etc. The DNR usually stays in affect so the pt will not suffer thru another attempt at resuscitation.
A Living Will, in most places, is a record of your wishes.If the above pt, with the brain damage and organ failure, has a living will on record with their family,doctor,lawyer,etc., it makes things easier for the pts family. They may elect not to start treatments such as dialysis, feeding tubes, ventilators. If the doctor has done everything necessary to see if there is any chance of a meaningful recovery.
The only times I have seen a Living Will keep a pt from being resuscitated is when an old, and I mean old, pt comes into the ER, usually from a nursing home. The EMS usually brings the pt in, while doing some type of resuscitation efforts. The nursing home finds the Living Will, the pts doctor and family is contacted and the efforts are stopped. Allowing the pt to "go on peace" as they wished.
I hope all my rambaling makes some sense. I am not a lawyer. only a Respiratory Therapist who has worked in a hospital too long (15 yrs) and has seen too many thigns happen. Make you wishes clear. That will in no way stop you from getting any help you need in an emergency situation. Especially a situation that has a "reversible outcome."
