This user's account (Evie0602) is exactly what just happened to me.
I also don't have any babies (unlike the original post). My Sims had the rat for about a couple Sim days. I just got the pack about a week ago (in real-world time). I fed the rat once; the game never let me feed it again, so I assumed it must not need to be fed often. Suddenly, I got a notification that the rat had died of starvation, but when I went to see what to do about it, the rat was "alive" -- had stats, said it was starving, moving, running on its wheel like a zombie with green odor animations coming out of the cage. I didn't have the option for my Sim to clean the habitat or release it, so I tried to have my Sim "purchase rodent" (to replace it). Nothing happened. So I tried deleting the cage (from build mode). It disappeared (I think?) but when I tried to buy a new rodent cage to replace the original cage, placing it in the same spot, the game completely broke. The cage kept switching between being visible and not being visible. I was in & out of build mode trying to delete it or fix it, so I can't remember now when it was visible (which mode) and when it wasn't, but in either case, I couldn't successfully interact with it via my Sim in live mode or successfully delete it from build mode. If I deleted it, it would come back. Then I'd go to replace it, and it would be gone, so I'd try placing another one -- couldn't interact with it, either. Then, I couldn't interact with anything -- couldn't click on it to delete it in build mode, couldn't direct my Sims to interact with the cage or to do anything else in their house. When I tried to exit, it wouldn't even save or exit, just froze on a loading screen for several minutes. I have two young adults on the lot, neither of whom is pregnant.