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One thing that we would occasionally do (and I don't know if this is a 'correct' thing or not) is if Odie was whining, we'd go near his crate and mooch around pretending to do stuff but ignoring him. It would often calm him enough just us being near, but we're not actually giving him attention so there's (hopefully!) no positive affirmation of him whining. That was my thinking anyway - he's pretty chill in his crate now and will go in on his own accord and not whine when we're not there.
When we adopted Crumpet, we were told to do your best to ignore your dog when they're whining or seemingly anxious, regardless of what it's about. It's hard to do but the logic is that by comforting and reassuring them, you're confirming to them that there's something to be worried about. By ignoring them and getting on with whatever it is you were up to before, it shows them that everything is fine and they don't need to worry. Crumpet cried a fair bit for the first few days we had her, particularly at night and it felt very cruel just leaving her to it but now she's a very happy, confident dog. We let her up for a cuddle in bed around 5.30 every morning after she's been out to use the toilet but other than that she's more than happy being left on her own downstairs now.