So...
They broke up, some time after this "Cat" entered Gf's/their apartment and was lying in a pool of vomit (page 35) and GF then states the page 5 line upon seeing her. At this point she clearly is quite delusional, probably not taking her meds and maybe even suffering from delirium tremens, hence the whole cat delusion. Eventually the gf realised this wasn't okay, she broke up with Cat for a reason and now taking care of her once more like a child or a pet isn't fine and ended up committing her to a mental hospital (without providing proper contact info, how is that possible!?!) after - presumably - her mother had come to pester her about it. Then Cat escapes and ends up wandering around until she falls to her death.
Bit sad towards the new partner, since I bet she was already with her while this whole episode took place. I'm basing this off on how they moved in together after "several days" of placing Cat under care.
An interesting read and a lot of environmental story telling, ie. the piano having been covered up and turned into just a decoration/shelf, a clear sign of not been in use for a good while.