Have they given you any specifics as to what the pet does to itself and/or the home?
Realistically, finding the dog another home most likely won't happen. They would need to be up front with the potential new owners and let them know the problems the pet has been having. Someone with experience with seperation anxiety may be willing to adopt them and put in the work, but just someone looking for a pet will not be willing to. A person can love animals but that doesn't mean they would be willing to adopt a pet and spend an unknown amount of money on it, risk potential damage to their home and belongings and have to spend hours upon hours of training for a problem that may not be able to be resolved.
Putting the pet on the bed is not going to solve the issue. The pet needs to learn to be comfortable with being alone, it does not need to be coddled. I use the term "it", which I usually don't like to do, because I do not recall seeing if you mentioned if it was a he or she. I for one, as a pet owner, do not allow my dog to get on the couch and definately not on the bed. I have allergies, I don't like to have to clean up excessive hair if I don't have to and the dog is on the bottom of the totem pole and therefore does not get to sit where the "big dogs" aka the humans of the house, sit. A dog is no less loved if it is not dressed it ridiculous outfits, is not allowed to sleep on the owners face every night and kick their husbands out of bed or steal food from their children's plates. Lol that's my soapbox.
I am not trying to sound as if it the situation is impossible, just showing both sides. It can be tiresome to have to deal with you work problems, home problems, family problems, child problems and not on top of all of that you have a dog that goes berserk because you leave the house. I hope they are able to work something out, but they need to seek the professional advice of a pet trainer, not the advice of family or friends or even their vet.