I don’t know if this is a new thing, but I’ve seen several of these recently:
In some cases these appear to be artistic viral campaigns while others are just people goofing around. I’m wondering if anybody has run across other examples in their neighborhood.
Seen it, but what I saw was spam for clothing sales, etc rather than anything “artistic”. I just ripped them down from where they were illegally posted.
I’m with you on the spam/illegally posted part…we just had the “Gov’t Seized Property Auction” guys roll through town and their signs are posted everywhere.
I’m more okay with the kind of flyers I posted in the OP–at least they add a little humor to my day.
Somewhere there’s a little kid out there who just wants their beloved burrito unicorn back, and who’s heartbroken that you don’t think poor Pablo is real.
an early Internet classic, I believe:
The fake ‘lost pet’ ones round where I used to live were mostly annoying ads, often for gigs.
A noticeboard in a local shop often got funny parody ads stuck up though, as the staff didn’t pay much attention, though I don’t remember any ‘lost pet’ ones. I think my favourite was the one which was roughly: ‘Local psychic: No need to call, we know who you are and we already have your number…’
I haven’t seen any fake ones, but invariably whenever someone new moves in around here, about a week later a “Lost Pet” sign shows up down by the mailboxes.
Like, the constant howling of coyotes at night haven’t clued you into the mystery location of Little Buster.
I’m gonna share this with Beckdawrek!
There is a faked picture about a woman finding a lost kitty-cat and giving it a bath. However, the cat is a mountain lion. 
(“Sorry you can’t embed media items in a post”)
These are NOT fake – which makes them all the more amusing!
You have to link to items that are hosted somewhere else, and they will be displayed inline in your post. But the board doesn’t support direct uploads.
Not exactly a lost pet, but close - Lost - 8 small strips of paper containing my contact info
The famous modern British artist Tracy Emin lost her cat and so posted many ‘Lost Cat’ posters around her neighbourhood.
Some people thought the posters must have been part of a new ‘art’ exhibit by her, and so took down the posters and some were sold for large sums of money.
There’s a “thing” in my neck of the woods. A weird little lost cat doodle that has been showing up a lot.