There is plenty of evidence for exercise of all sorts to improve cognitive function in later life. That outcome might be mediated via increased blood supply to the brain, which is a particularly energy-hungry organ. Or it might be mediated via improved mitochondrial function, for much the same underlying reasons relating to energy demands. Or via any one of a number of other related mechanisms that one can link to exercise. Strength training is thought helpful in yet another way, via building or retaining muscle mass that then in turn alters metabolism in favorable ways (that usually lead back to blood flow and mitochondrial function in some way).
There is some overlap between researchers interested in strength training and those interested in ischemic conditioning, a form of intermittent restriction of blood flow that appears synergistic with exercise. One can view this all from the perspective of triggering stress responses. Exercise triggers stress responses, and so does transient ischemia. The former is far more explored, and the latter is harder to undertake safely. One might also view this area of research as the preliminary exploration that leads to drug candidates somewhere down the line, ways to artificially trigger beneficial stress responses, but I think that the past few decades of work on calorie restriction have demonstrated that to be slow, expensive, and challenging.
The integrity of the musculature and the muscle strength is of great importance throughout the entire life span. Age-related decreases in muscle mass and strength are also associated with morphological losses in the brain and decreased cognitive functions. There is growing evidence with respect to positive effects of physical activity preventing and treating morphological and functional losses in muscles and the brain. In recent years, evidence has emerged emphasizing the existence of a bidirectional relationship between physical performance and brain health. The bidirectional relationship suggests that physical training may be a valuable intervention strategy to decelerate not only physical but also cognitive decline in old age. However, the exercise type (e.g., resistance training, endurance training) and exercise variables (e.g., load, duration, frequency), which would be optimal to efficiently enhance cognitive performance are largely unknown.
A promising and cost-effective physical intervention strategy which preserves and enhances both, physical performance (especially with regard to the musculature) and cognitive functions, is resistance training (also known as strength training). A relative new method in the field of resistance training is blood flow restriction training (BFR). While resistance training with BFR is widely studied in the context of muscular performance, this training strategy also induces an activation of signaling pathways associated with neuroplasticity and cognitive functions. Based on this, it seems reasonable to hypothesize that resistance training with BFR is a promising new strategy to boost the effectiveness of resistance training interventions regarding cognitive performance.