While there's very little concrete evidence to support this, there are theories that a garbageman viewed briefly in Toy Story 3 is actually the malicious Dr. Frankenstein-of-toys Sid from the first film. The main visual proof is that he wears a skull shirt, similar to the one Sid wore, and that the general ages seem to about match up (also, it's the same voice actor, so this is pretty certain to have been meant as a fun wink at the audience). But the behavior of the character seems to speak to it being Sid so much more than anything else.
Remember - Sid knows that toys are alive. As far as we know, he's the ONLY character in the Toy Story universe who possesses this knowledge. But what has he done with this terrible understanding after his traumatic encounter with Woody in the first movie?
He's become a garbageman - but not just any garbageman. He's a garbageman who HATES toys. And it's certain he's told his fellow garbagemen to keep an eye out for disposed of toys - and make sure they are either destroyed, or suffer enormously. He's told them toys are alive, and could turn on them at any moment.
What evidence is there for this? Think about the ultimate fate of Lotso in Toy Story 3 once he's picked up by a garbageman colleague of Sid's, who owned a Lotso as a kid. Despite his fond memories, THIS is what he does to Lotso:
This is pretty much the toy equivalent of being crucified. And it's all because Sid knows the terrible secret of toys.
That's why Sid became a garbageman - it was the most effective way to destroy and torture as many toys as possible and get away with it. He knows normally most toys would simply be left to rot in a landfill...where they could possibly escape. Sid makes sure they meet their fate in the incinerator, or are crucified as a warning to the other toys of the world.
Like, in every movie, the toys will go to the ends of the Earth to save one another to keep their weird "family" together - but in Toy Story 3, Woody's just sorta bummed that the supposed love of his life is gone. Did she simply get sold at a yard sale? Thrown away? It seems pretty unlikely they wouldn't have mounted a huge adventurous search party to bring her home...unless she was destroyed or something, and they knew that their search would be fruitless.
So yeah. Bo Peep's probably dead.