It is hard for me to imagine someone who has lost a loved saying this to another person who is grieving. I could imagine them saying "Take care of yourself" (as in, making sure you eat, shower, etc) but not "stay strong." Another DISer may come here and tell you that they in fact have experienced grief themselves and have said this to other people before, but in my view the grieving process is one that leaves most very vulnerable and it's not feasible or possible (or possibly even healthy) to "stay strong" in the beginning.