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There are a few things that can cause your cat to drool excessively.
Cats will drool if they feel nauseated but not to the point of vomiting.
They will also drool if they have mouth pain from a possible tooth or gum problem. Take a look in his mouth but you might not see anything. Sometimes tooth pain is not noticeable.
Sometimes they will drool if they have ingested garbage or other irritants and WILL drool if they have ingested poison.
I think that you should do your best to move the bed out of the way, retrieve the cat and see the vet as soon as you can.
Let me know if you have more questions.