It isn’t that easy a problem. Not all blood borne diseases have cures, herpes simplex for example.
My 68-year old mother had part of one lung removed due to cancer. She required blood transfusions, one of which was tainted with herpes simplex. Not cool.
I’m very sorry for the death of your mother. Nothing can mitigate the suffering she endured nor the sorrow you feel.
But, if the only blood available to save someone is unscreened AND the patient will die without the blood, I would take that risk. Die today or maybe die tomorrow? That is the choice given sometimes.
Please accept my condolences for what your family has experienced. I wish that the suffering had not happened.