I'm so sorry to hear of your loss. Is your yard fenced or were they tied out? If it's fenced and you think someone is opening the gate to let them out, try getting a padlock for the gate. In the meantime, keep your remaining dog in the house while you're at work. As far as the depression goes, I do know that there have been cases where getting another dog has helped the remaining dog with their depression. I know that when we had lost a dog while I was growing up, my parents had always gotten another one as soon as possible. It really helped us with the mourning. Of course, we never forgot the one that had passed on. Nothing could replace the ones that have gone to the Bridge. Having said that I have to say that you are the only one that can tell if you're ready for another dog right now.
Again, I am so sorry for what you've had to endure. My heart aches for you.