I was cleaning off a shelf in the basement and I noticed that the area under my bleach 1 gallon container was all crystalized. It had been there about a year, and when used last it was approximately 1/2 full.
When I lifted it up today the cap was on tight, it was completely empty, and the container had sucked in on itself. The container was all crystallized around the lid, and dried crystals were all over the sides of the container.
On the shelf below this I had a Le Crueset porcelain stock pot with the lid on it and it had caught most of the dripping from the above bleach container. This pot had also become all crystallized on the outside, and when I lifted the lid I found that where the stainless steel rim of the pot lid had been in contact with the top of the pot it had became badly corroded.
The screw for the pot handle had also become badly rusted and in the bottom of the pot I found what appeared to be about 1 cup of highly concentrated bleach.
This whole shelf had been standing approximately 2' from our basement dehumidifier.
Is it possible that the dehumidifier caused the bleach to be siphoned out of the plastic bleach bottle? and, are there any other cleaning products that this may happen with?

It's not the dehumidifier. It may lower humidity to 30% or so if you're really overdoing it, but quite a few places the indoor humidity is lower than that naturally in the winter.

This wouldn't happen to be one the brands recalled last year, would it?

I do not understand your answer can you please answer my question?
I checked and my dehumidifier was not on the recall list.
What does the humidity level have to do with what I had described happened to my bleach container?

I'm sorry I wasn't clearer... My answer to your bolded question is "no", and the rest of that first paragraph is why I believe that answer to be correct: it is naturally drier in many places than your dehumidifier could ever accomplish, and bleach stays in the bottle just fine in those places. Therefor it is unlikely to be the dehumidifier.

The part about the recall list (I should have been clearer here) was about your bleach. Is your bleach on the recall list? (There were some brands recalled not too long ago, I think sometime in 2007. The were recalled because they could explode, and if yours is one of them, that'd explain what happened.)