I think a more accurate question would be: 'Where will our consciousness reside when we no longer have a physical body?' For when you say 'a person's spirit when they pass away' you make the assumption that the spirit 'belongs' to us. My contention is we ARE the spirit. The 'I' that looked out through your eyes and saw the world at two years of age is stil the same 'I' that looks out through your eyes and registers a 'world out there' today.
Do not make the mistake that you are your physical body, or even your mind, for that matter. The physical body is changing constantly and the matter that makes it up arises and passes away with the more rapidity than bubbles arising in a glass of champagne. The part of you you regard as you, your physical body, that gets into a shower in the morning, is not the same body that gets out of it a few minutes later. It might appear to be. But it is not. You and I are changing, changing all the time. This is how we grow into adulthood, live our life and then 'die.' The patterns of what we think we are are constantly changing.
We are not our minds, for our most precious beliefs can change over time, and we know we are something CONSTANT. We are the Observer. We are the Witness. We are the Experiencer.
What do I think that happens when we die? We don't die. However, the new environment in which we find ourselves - and that is the question I think you're really asking - is that we will be SOMEWHERE. We will still be observing, witnessing and experiencing. It's a change we must all go through. The question is: Do you fear that change? Or are you sorta looking forward to it as another great adventure?
Your attitude, your Life Philosophy on this most important matter, will make all the difference between a meaningful and and meaningless life. Be sure to pick the one that will bring you happiness.