I’d take that risk with a family member.
And you’d be wrong. I’m a neatnik. But the idea of throwing away stuff against the wishes of the old lady would be anathema to me.
I’d try to persuade her. But failing that the stuff would remain. She’ll be gone eventually and the stuff can go then. I see no rush.
This seems like the approach that would work (and the OP’s dad should have accepted those old schoolwork papers). It might be a little long-range, though.
The OP really needs to have a heart to heart talk w grandma. Much more to listen than to persuade.
Is she saving things because of mental illness, Depression-era scarcity mentality, the fact that each thing is an irreplaceable memento, simple inertia versus a huge task, or as a favor to other family members who’ve treated her house as the designated warehouse for decades?
By exploring these issues with her, you can discover what she’s thinking and perhaps help her to drop any less rationale reasons she may be clinging to out of habit or self-ignorance.
Only then can you do the right thing by her lights.
Assuming she’s not dangerously senile or certifiably insane your only legit goal is to improve her welfare as she sees it. That may involve less moldy junk in her basement, and it may not.
Good luck. It’s neither simple nor easy.
I don’t want to sound snarky but I wouldn’t commit a crime against a family member.
I can accept that some people have hoarding problems. But I strongly disagree with the idea of going behind their back and unilaterally deciding to throw out all of their possessions that you feel are worthless.
First, I don’t like making the assumption that I’m capable of deciding how other people should be living their lives. I sure as hell don’t want other people making decisions about how I live my life.
Second, the problem here is the hoarding not the hoard. If a person has some mental issue that makes them accumulate stuff then suddenly losing all that stuff - regardless of its objective value - will be a mental trauma. Throwing out a hoarder’s hoard is the equivalent of locking a claustrophobic in a closet.
Third, if you just throw out the hoard without addressing the problem, the hoarder will still have the problem - and will just start accumulating a new hoard. Except now the hoarder can add paranoia over somebody stealing their stuff again to their existing problems.
I agree – on those shows the therapists always make sure to get the person’s buy-in and help them work through their issues at letting things go.
I have to admit when my brother went into the hospital years ago, my parents and I cleaned up his apartment, partly because we would have had a hard time staying there otherwise, partly because it wasn’t how we would keep it. (He’s not a hoarder, just lazy – he had a layer of scrap papers and stuff covering the floor, empty cans and bottles, etc.) When he went back he had anxiety and panic and I always felt that us changing his apartment may have contributed. He did later thank me for helping him through the whole ordeal but I still feel bad about it.
(He also had toenails so long they curled over his toes, and I had to restrain myself from trimming them while he was unconscious. 
I did realize what an intrusion that would have been.)
Buy a few mice and stick them down there, then tell her, she’s gonna have a lot more of them if she doesn’t get rid of all the junk down their giving them a nest.
Snapping pictures can sometimes work, too, especially for three dimensional things that won’t scan.
I’m trying to remember the name of the book I found another idea in. That’s the idea of thanking things for being part of your life and letting them go, either into the trash or to a thrift store. The book was written by an organizer who made her clients touch the things that were being sorted into things to keep or things to go. While they held the object they had to ask, out loud, does this bring my life joy now?
Remembering that the thing brought joy in the past is not a reason to keep it. It has to bring joy now.
You could make a recording of your grandmother talking about the memories that different things call up. The memories don’t have to go just because the things go.
If you do it now, with your grandmother, you’ll get the stories. You won’t have the stories if you wait until she’s gone.
I just read that book. I agree that it had a different and more resonant approach than the usual advice.
The book is “The Life-changing Magic of Tidying Up - The Japanese Art of Decluttering and Organizing” by Marie Kondo. Here it is on Amazon: http://www.amazon.com/Life-Changing-Magic-Tidying-Decluttering-Organizing/dp/1607747308/
My mom had a hundred or so photo albums, covering maybe 70 years of the family. When we cleaned out her house, we divided them up to scan and share. It has been a labor of love that we so far have neglected to carry out. Sweet idea, though.
You may be able to get this done commercially for $Not a Lot.
That would be wonderful. Even listening without the recording would be wonderful. Family stories are irreplaceable.
Can I point out that there is no reason to think Grandmother is a pathological hoarder? She could just be a normal woman still living in the house she raised her children in, with a little more space than she needs and a lot of worthless items of great sentimental value, who was kind enough to store the stuff her children don’t want to deal with, either.
Even her storing those boxes won’t seem so ridiculous when it comes time to ship some of that stuff off to Uncle. Good shipping boxes are dear.
Underlining mine.
I agree with you that several posters have assumed grandma is a hoarder when it sounds much more like what you (and I) have said: she simply has 50+ years of normal accumulation. Until one runs out of storage room there’s no deep need to not keep stuff. The path of least resistance is simply to cart it downstairs & stow it. So far, so typical. And so harmless.
But I wanted to talk about the part I underlined.
Every item in that basement was used at some time by someone in that household: her, her husband(s), or her kid(s). But not everything has “great sentimental value.”
And therein lies the trap for lazy-minded folks. Yes, that was Jimmie’s train set from when he was 10. And yes, those *were *hubby #2’s favorite house slippers from when he was 40 back in 1970.
But she hasn’t thought about those specific items in 50 years and had forgotten that they were in the basement. Seeing them will bring back a memory of what they are. And that’s pleasant and nostalgic. And at that moment throwing away a memory-jogger seems heartless and painful.
*But the thing isn’t the memory. *And the thing isn’t necessary to retaining the memory; that memory was there in her head all along. We just proved that.
Breaking through the wall of mistaken belief that “discarding the item discards the memory” is tough. But once a person recognizes that as a fallacy, they cease being prisoners of the pile of stuff they’re otherwise stuck curating.
It is true that each such item is irreplaceable. But the error in thinking is to raise that irreplaceability to an unassailable virtue. Yes, you’ll never be able to get another pair of your late husband’s slippers. But why would you want to?
It’s also true that most such items are just items. Some things truly are mementos. e.g. High school graduation pictures of the kids. But the sneakers they wore that same year? Not so much.
If a person doesn’t see the difference it’s probably because they’ve never had to think about the difference before. A little patient counseling can do wonders here.