Okay, so.... the cat has split into multiple versions of itself. What do I do now?
Just simply playing in the browser. I was clicking on the toilet and toilet paper when the browser slowed down with a stutter as you may expect browsers to do every now and then. And as the lag was clearing, I saw it split into multiples in doing the animations.
All cats behind earlier cats could not move into where their future cats were.
I ended up playing around with them a bit and found that the future cats, when looping back from fear of the kitchen sink melded into the other cat waiting at the back of the queue.
Yep, so it originally occurred directly after I flushed the toilet while the cat was beside it. I attempted to replicate it on a second playthrough, but it didn't occur. It was corrected by repeatedly doing the tasks for the black cat up until the full sink, but without the TV. When they met at the bathroom door, they would meld again, first so there were two, then leaving one. I was able to complete the game normally afterward.