Since we're forced to accept certain elements of the hybrid as being canon, we have to start with Elly trying to stave off Mike's need to have a dog by buying him an endless series of goldfish. When that didn't work, we ended up having to deal with the end result of Mike finding out about Mrs Baird, her prize sheepdog and said pet's final litter. Since John said all the right things (and, I suspect, made someone who dreaded becoming the sole caretaker of a pet she never wanted into an ogre), it was easy for the old doll to make up a convincing lie that let Elly's need to feel guilty work against her own interests. The rest is history as well as tragedy as what could have been a great dog suffered from the witless, shiftless malice of wooden-headed owners who never paid him attention unless he did something to bother them and who died a stupid, needless death because no one had the sense to keep track of April was.
Speaking of the pea-brained negligence that almost resulted in April's death, we have to remember that while Edgar did alert the stupid bastards to the fact that the poor child was fighting for her life, we also have to remember that he's also the end result of the same sort of stupid refusal on Elly's part to monitor April's actions that led to this mess in the first place. If Elly could be asked to be a parent instead of whining about being tied down, we wouldn't have another dog to be kicked at, April would also have never gotten near that river in the first instance. The same sort of malicious stupidity must have come into play when he passed away; I don't see him dying by getting hit by a car or pulling a child out of a well but he probably has passed on because of illness or old age by now. Since he was under the 'care' of an idiot who plays with trains and an inattentive old bat with a cleaning fetish, what I do see happening is their only noticing he'd died when they tried kicking his ice-cold remains out of their way.
As for Dixie, she seems to set another precedent; that's because Jim's neighbor couldn't take her with him to the rest home so gave her away to someone reasonably responsible. While it's true that Jim knew what he was doing, it's also true that when he too had to surrender her, he gave her to his idiot daughter so maybe he's not that good. (Especially when you consider that her death was akin to Eddie's.)
This makes Jim akin to the first person to own Butterscotch. As we know, she's introduced as a rabbit that someone in April's circle had to give away because he couldn't take care of her. He should have tried harder to find a new owner because once again, the Pattersons' inability to anticipate problems led to the poor thing being "amusingly" electrocuted. Given how stupid John and Elly are, this means that she either died like Edgar and Dixie or they gave her away and told the Martian she died.
Sadly, we come full circle when contemplating poor Shiimsa. That's because she's the end result of the equation "Abandoned kitten plus emotional blackmail equals stupid woman with cat." What makes Liz stupider than Elly is that she can't seem to remember that her mother is terrified of cats owing to some unknown incident in the past. I personally suspect that shortly after the Settlenuptuals, the poor thing ran off and got taken in by competent caregivers. While the Martian might have objected, no one else seemed to be that worked up.
This is sort of a bummer because in the five years since we last saw the Pattersons, it is very likely that she's the only of the pets who is likely to still be alive. This means that by 2010 at the latest, Elly finally got her nice, cozy pet-free life back. It also means that while she's watching Connie walk Sera 2.0, she's looking back on a career of being a great pet owner. After all, if she can mythologize how great a time she had with Farley, she can do the same for the other pets subjected to her abuse and martyrdom.