Yes...that's why I made sure to get another dog before my old dog dies; plus, to give myself enough time to get securely bonded with her before I have to deal with accepting the loss of my older dog. It's also why I have two cats. I once had two birds not too long ago, but I ended up loosing them both at the same time, so that too can happen. However, having my other pets did help a little. I had to cover up where the birds' cage was with plastic and I've never taken that plastic off yet (in my dining room no less). I can't even bear to look at that piece of furniture the cage was on because it still upsets me even years later!
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"Has not my hand made all these things, and so they came into being?" declares the LORD. "This is the one I esteem: he who is humble and contrite in spirit, and trembles at my word." – Isaiah 66:2