Everyone has experienced some sort of loss which has left them in grief or some other similar state. Thing is, there are often two sides to the situation.
There is of course, the person who has just entered the state of loss. And there are the people around that person - friends, colleagues, relatives, and so forth, who are looking in at the situation from the outside.
Let's look at the latter, first.
Most people who are looking in from the outside have, themselves, experienced loss and grief even though they may not currently be there. However, because they had at some point experienced a loss, they do know the feeling (in their own personal way).
And, because they have empathy for the situation, many people will offer some sort of condolence. It may be a few words like: "I'm sorry to hear about your loss" or "They are in a better place." Rarely, will these kinds of statements really offer consolation to the grieving party however it should not be looked upon as what is said as much as the fact that other human beings had empathy for your situation.
Why is this the case?
Well, this can best be answered by talking about the person who is currently grieving. A very popular resource in the grieving process includes the concepts of Elisabeth Kubler-Ross who proposed the five stages of grief; denial, anger, bargaining, depression, and acceptance. The person who has experienced recent loss may be in any of these stages and it's not always easy to tell which one. So when an outside person attempts empathy, it may or may not be well received depending on the stage.
Thus, the person offering empathy may be rejected or even yelled at for their effort and the person experiencing loss may feel insulted by what they perceive as insensitive or inappropriate comments. Thing is, it could all be because of the stage of grief the grieving person may be experiencing at that moment.
With this, for those offering empathy, know that it's not about the response but about the effort. And for the person in grief, realize... maybe at a later time, that people in your life had cared enough to reach out. You might not be able to receive it at the time it was given, but eventually, you might see it. And when you do, you can know that people truly do understand!