Two of our girls, Meko and Jacqs, understand that we occasionally have to go out and they need to stay home. They don't like it, but they have come to accept our way of life and usually relax and sleep while we are out.
Our newest girl, Kitsune, who we have had for a little over a year now, was six years old when we got her. We don't know a lot about her but we were told some of the circumstances that led her to us. She had an owner who died and then she lived for a year, before coming to us, with a foster-care woman who also had a 2-year-old grandson around a lot and a few other small dogs. Kitsu spent most of her day under a bed.
I think she is very happy living with Jim and I, our other two dogs, Kameko and Jacquay, and our cockatoo, Coco. She seems to be fitting in just fine, until we go out.
Jim has told me that when I go out for the day, she spends most of her time barking until I return home. I think she does that, also, when he and I both go out together and leave the pets at home.
And when we return, she barks and gets very excited, jumping at me for attention. I believe this is 'separation anxiety' behavior. I ignore her barking until she calms down, then I give her attention. But I don't know how to keep her calm when I am not home and somehow reassure her that we will be back.
I did my usual research on the internet but found most of the situations around separation anxiety dealt with people who had a dog from the time it was a puppy and they usually went off to work for the day. The recommendations were to take the dog for a walk before you leave for the day. Since Jim and I are both self-employed, we don't have a regular work schedule and don't always know when we will be going out and for how long. I also read to leave your pet with a piece of clothing that you recently wore that has your smell on it. This may reassure your pet somewhat. I have not tried this but don't have many articles of clothing that I would wear and also let my dogs lay on (they are very hairy!)
Another thing to do, that I do make a habit of saying to my dogs, is that I'll be back in a little bit. They know, then, that I won't be long. I'm not sure Kitsu is paying attention when I say that and has made a connection to what it means.
These are a few tips to use. I have no interest in other suggestions I've read to use drugs to reduce anxiety when we go out. I prefer to try all other natural solutions first and never consider medication a viable solution. Hopefully some of these suggestions will help with your anxious pet.