Yes, recent studies show that even the most exhausted T cells can be rejuvenated. 

Earlier, it was thought that T cells could not be rejuvenated after they reached a point of exhaustion. However, researchers at the University of Pittsburgh and University of Pittsburgh Medical Center have shown otherwise. 

When T cells get exhausted, they lose some of their functionality, which impacts their ability to fight off pathogens and infections. Some immunotherapy drugs can help boost the immune system and remove the checkpoints or brakes that inhibit exhausted T cells. This can reinvigorate the exhausted T cells and temporarily restore at least some of their functionality. 

The extent to which exhausted T cells can be revived depends largely on the timing of the intervention. The earlier in the process the intervention is carried out, the more durable the benefits. Contrary to the earlier belief that T cells could not be rejuvenated after a certain point, new studies suggest that it may be possible to revive even terminally exhausted T cells by through co-stimulation or by engineering CAR (Chimeric antigen receptor)-T cells that can overcome the effects of hypoxia.