I guess it's different for everyone. I lost one Grandfather when I was 12. I was closest to him. He was a dirt poor farmer and didn't own a thing. He lived in a house for free in return for farming a man's land. He didn't running water or a bathroom until I was about 9 or 10. I can still remember having to go out into the pasture to the outhouse. He always wore a hat, not a baseball hat, but a hat with a brim all the way around. When he passed away, I didn't want anything from his home, but then again, there wasn't anything to get. It wasn't until I was about 40 that I wanted his hat. I asked my parents about it and they said they had thrown that old hat away because it was so filthy. Right now, I'd give you about anything you wanted if you could provide me with his hat.
For most of my adult life so far, I didn't have much interest in my family tree. Several years ago, something sparked it in my and I started looking into it (I think I posted some stuff about it on here), and now I care a great deal about all those things I never cared about before. My advice to anyone that has family that says they don't want things, is to box the stuff up, label it the best you can (what it is, where it came from, who's it was), and ask them to pass it along even if they don't want it. At some point in someone's life, someone will be greatly interested in it and that box or those boxes will be more valuable to them then you can ever imagine.
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Real name Steve but that name was taken on the forum. Used Middle name. Call me Steve or Scott, doesn't matter.