Before I get painted as a callous Michael Vick type... I have two dogs, both of which I adopted from shelters - one even though it has heartworms and might not survive them. I have no doubt they would “miss me” if I got hit by a bus and never came home again. But in the same way as I will miss the one with heartworms if it doesn’t survive? No.
I’m frequently amazed at how dogs conform to their masters and become “creatures of habit”, and also at how they behave in ways similar to man. It’s that similarity in behavior that lends itself so easily to anthropomorphism. But to conclude that similarity in behavior demonstrates similarity in cause (e.g. emotion) is an assumption without foundation.
When I say that my car doesn’t like cold weather, or that your plants seem happy, you understand that I’m referring not to actual emotions but to behaviors or attributes in some way resembling those of man.
This nonsense about dogs’ “grieving time” and “needing closure” and so forth is a trick of Darwinian atheists playing on our emotions - and on our epidemic loneliness in this ever-more-DISconnected society.
Sorry to hear about your dogs having heart worms, but when I was growing up there was no way to prevent heart worms and the cure was about as bad as the disease; so most dogs were put to sleep when they got too sick. Having said that, most dogs had the disease for years and years before needing to be put to sleep. Our neighbor’s dog lived seven years between diagnosis and death. Since it was so common, no one thought much about it.