Kirby will do that if left out. Normally I crate him but I've been starting to trust him for really short outings and he seems to just park infront of the door. He will also do that if someone else is home but he has gotten better at letting other people distract him (especially if they are offering treats/belly rubs). Initially when I got him he also wouldn't touch his food (not even treat filled kongs) while I was gone. Must admit that worried me a bit because in my opinion he was stressing more than I wanted to see, especially since I think he would also spend the time sitting and staring without relaxing enough to rest while I was gone. Slowly however he has started to trust I'm coming back, but I have a feeling he will always be a velcro baby who just kind of plop and wait for me to return.
One thing is when I do greet him they are always real low key, no barking, whining, pawing, or jumping up. Because I felt he was verging on the edge of separation anxiety when I first got him, I made a big deal about ignoring him when I would first come back and I think it has helped him see me going is not the end of the world. Plus it is nice to come home to a dog who will greet me real calm even if I know he is all excited on the inside.