This is obviously a preference thing, but I would strongly recommend against encasing Bubby in carbomite.
I understand the sentimental value that these things have. The problem is that such a thing that the kids had forever (that gave them a little bit of security and familiarity in not so secure or familiar situations, like visiting relatives or an overnight when the aunt baby sat) is that the attachment has to stop cold.
You're quite literally taking it away. It's no longer Bubby and it's turned into a keepsake. They will no longer be allowed to simply interact with it.
My 20 yo had a crappy, wal-mart, Power Ranger comforter that his mom got when he was < 5. They had it when we got together. When he went to college he took it with him, tattered, stinky and flat. When he moved from college into his apartment, soemthing happened and it got ripped horribly and lost all it's usefulness. He brought it to show his mother and we all lamented the loss of his bubby and he put it in the dumpster. The wife got it out, salvaged several good sections and made him a blanket that we gave him for xmas. And we all laffed.
It will fall apart, but it will increase in value as it falls apart from use than it will ever have sitting on a shelf as a keepsake.