Human Stem Cells and Disease
Stem cells can be stored but that is an expensive alternative to generating them freshly. It has been shown that you can make stem cells from skin cells. 

Theoretically, it would be much less expensive to store a piece of epidermis from a recently deceased relative than to make fresh stem cells and store those. 

However, the research for generating stem cells from deeply frozen tissues is not there yet. Furthermore, the concept of using stem cells to 'combat disease' is not the right paradigm. It might even be said that some diseases (cancer) are the result of dedifferentiation gone awry. 

Where stem cell transplants are used is in the replacement of bone marrow after total body radiation/chemotherapy to destroy marrow (in those cases where the disease has arisen in the marrow). In these cases we rely on the poorly defined process that allows cells to target their microenvironment. 

For example, it would not work if marrow replacement cells decided to grow wherever they landed (lungs, liver,etc). 

So stem cell storage is an option whose time has passed ,as our tech now allows us to make them.