Benext,
I'm sorry to hear about your relative and the stress it puts on you.
First of all, we cannot make decisions for other adults. They have the right to decide what type of medical treatment they receive.
Unfortunately, this is a bad time to convince a relative that it is ok to take blood. About the only thing you can tell them is that it is no longer a disfellowshipping offense to take blood. They may announce you have DA'd yourself from the decision you make regarding blood, but it is a slippy slope where the blood issued is concerned currently with the JWs.
As far as how low can the red blood count of Hemoglobin go before there is damage to tissues of the body, especially the brain, there is no set answer or number to that question. There have been experiences of people who have low (2) hemoglobin counts that survive, but I notice there is no mention of quality of life or daily function after such an occurance.
What you describe as "injections" maybe a blood product that is approved by the WTBTs, erythropoeitin. It stimulates the production of red blood cells. But JW's cannot have another blood product, red blood cells, the oxygen carrying component in blood. Sad that it has come down to splitting hairs on what blood products are ok and what are not. Life is precious and to maintain it would seem most important.
Some hospital committees know that a cow's blood product, even though experiemental, has been approved by the WTBTs. Hemeopure. But it is not readily available.
About all you can do at this time is be supportive of whatever decision your relative has made regarding his/her life. This is a very painful time and so avoidable. All I hope is that you have love to show all, no matter how you are treated, no matter what decisions they make.
Please keep us informed.
Joy
edited to add: thank you iamallgrowedup for posting that document. Not many JWs know about it. But it was written so that JWs would not be viewed as a "cult" in Europe. Interesting that the R & F have no idea what it really means. *sheeesh*