After having gone through a lot of loss in the first few months of this year (my father in January, my father-in-law in March), the term that has been used when people talk to me is "Sorry for your loss". And that actually is the most appropriate thing to say.
As a psychic medium, I know that the end of this life is simply a return to real life. It is not sad that someone is out of pain, and has been freed from the trappings of this existence. It is not sad that they will not be able to reach a certain age, or didn't get to experience certain things. That was part of the plan they made when they came to this life. The loss is not experienced by them.
The loss is experienced by us, the ones left behind. A person of my gifts, I know that these people are fine and well. The loss is of not having them in this physical reality, this life. It is the change in routine, the thoughts that pop up, the feeling of emptiness that causes sadness. And the loss of their presence leaves a hole that hopefully is filled by something else over time. But it is OUR loss.
And to that, we offer condolences and energy. I also offer a shoulder, or an ear. But mostly, I offer energy to help one through the adjustment period, and it is just that, getting used to a change in our environment.
And to those that offer their condolences and say "sorry for your loss", thank you for your concern, your energy, and care.