I wouldn’t have considered myself a collector as such, even though I do have many fiction books from authors I like. There is a reasonable large number of them. And I also have a lot of non-fiction books of a particular theme (movie making). They’d certainly count as a response to the OPs conversation, though.
Oh, and my DVDs. I have a lot of them, but I stopped buying those 15 years ago.
However, very recently I started collecting Lego, so that definitely counts.
I collect fridge magnets from places I visit. I like looking at them and thinking, “Oh, yeah, that stuffed fish is from when I took my nephew to the Monterey Bay Aquarium and bought him an otter stuffie from the gift shop, which he named Brownie.” So they kinda have a purpose.
They don’t fit on the fridge anymore; I display them on metal plates hung in my hallway.
Lol. I am not overrun with owls, but for a while i was amassing owls for much the same reason.
I worked with a woman who had a similar story about Tigger. Someone bought her a Tigger shirt as a young teen and it looked cute so she’d wear it. This made everyone think she was into Tigger and it snowballed from there. She told me that everyone thought of her as “The Tigger girl” and kept giving her Tigger shit and she didn’t really care about the character at all but didn’t see a way out at this point.
Oh, my god. My situation isn’t nearly so dire, not even close, so I’ll count myself fortunate!
The most recent gifts were a pair of dachshund socks, which will wear out and I can dispose of them, and a breathtakingly bad oil painting of my first little guy. It makes him look psychotic. A+ for thoughtfulness as regards sentimentality. D- for execution.
I’ve no idea what to do with the painting. Bearing no real resemblance to my beloved late pet, it creeps me out. For now, it lives in a closet and will only be displayed when my friend comes to visit.
For people inundated with unwanted Tiggers, owls, dachshunds, and the like, I believe it was Miss Manners who suggested unwrapping the latest present in question and then saying enthusiastically and firmly, “Thank you so much! And this completes my collection.”
That’s incredibly awkward. Does this friend paint often? A home made painting seems like an unusual gift.
So many “collectors” seem to have gotten that way by supposedly well-meaning, but mostly clueless, friends.
And by being doormats unwilling to say “No, I’m sorry, you’ve misread me; I hate owls. I love my friends, but I love them more when they don’t give me stupid owls.”
She does. I paint a little myself, so I kind of understand the desire to give away finished work. It piles up pretty quick. But I’d rather throw them on a burn pile than inflict them on others, unless someone specifically oohs and ahhs over a piece. Even then, I ask, “Are you sure you really want this in your house?” Because I barely do!
Oh, i collected the puzzles myself.
The owls were all gifts, but i didn’t hate them. I was just bemused that people kept giving me owls. I think most of them stayed at my parents’ house when i moved out, and then got trashed when my parents downsized.
That’s a giftgiving strategy that I have honestly never understood. I just don’t get the reasoning behind the inference that if an acquaintance owns a dachsund, or owns one painting of an owl, etc., then that must mean that this creature is somehow their cherished personal totem of which they yearn to display a replica in every possible form and place.
Nobody has ever tried to give me additional versions or simulacra of a particular kind of thing just because I already have one of it that I like.
People just aren’t that imaginative, I think.
I always try to give only consumables, things that have a “use by” date. Foods, wines or liquors, calendars, candles, things my recipient can either enjoy or re-gift if they prefer. I’m never going to look for them to be displayed in their home. Nothing permanent. It’s been a good strategy.
Most people at my time of life are looking to divest themselves of possessions, not add more to what they’ve already got.
Display it in a place of honor for two or three visits, but without remarking on it in any way unless she brings it up, thus giving the impression that this cherished painting is now an integral part of your life and a highlight of your home decor scheme.
Then disappear it and continue not mentioning it. If she notices its absence on a subsequent visit and asks about it, explain with mild regret how it fell victim to some lamentable and irreparable accident. But—key point—don’t seem too upset about your loss, which might inspire your friend to offer you an equally unwanted replacement.
We’re on the same page. 
I’ve already constructed the “accident” that will befall it. It involves the current dachshund managing to badly chew a corner of the painting of the former dachshund. The current dachshund is bad enough to do it, too.
I completely agree with not bringing the mishap up myself. I doubt she’ll say anything, but I’m ready if she does.
Is accumulating the same as collecting? I have about 15 long boxes of comic books but I only bought them to read them. The first young person to show a genuine (not financial) interest can have the lot.
I also have a collection of (four) pinball machines and (four) surfboards. They all still get used.
Commission several exact reproductions of the painting, each successively decreasing the original size by 10%. Swap out to a new painting each time she visits.
Well planned! And of course I hope you will brief the other residents and/or frequent visitors sufficiently that everybody knows not to say “oh, I see you’ve put that weird dachshund portrait up again.” 
That’s just asking for 2 new paintings - 1 for each dog!
Nah. If she offers to reproduce them, I’ll just honestly say that I am out of space to hang them, and I’d rather we simply remember her original effort for the thoughtful, kind gesture that it was. If she feels the need to reproduce it, I’ll visit it at her house.
No, I really don’t think it is. Collecting is done with intent, and accumulating seldom is.