Warning! Major spoilers for Run below.
One of the first shocking twists in Run comes when Chloe realizes her mother has been giving her dog medicine, which opens up a plot hole considering the family dog has been mis until that point. This revelation is confirmed by their pharmacist, who tells Chloe that the medicine in question is for her dog. But why isn't the dog ever shown onscreen?
Run follows the daily life of teenager Chloe (Kiera Allen) and her doting mother Diane (Sarah Paulson). Chloe's body is riddled with various illnesses, so she's in need of constant care and supervision. However, once she finds something peculiar about one of her new medications that gives her cause for concern, Chloe begins to investigate. She takes the little green pill to her pharmacy, where it's confirmed to be for her family dog, not humans — and not even for her or, as she earlier suspected, for her mother. This reveal is made even more shocking by the fact that Run makes no mention of Chloe and Diane even having a dog, nor is there any evidence of one around the house.
The reason for this is because the dog was all part of Diane's ruse in the Hulu movie. Chloe's reaction when the pharmacist tells her the pill was meant for a dog says it all. It also goes to show how far Diane was willing to go to protect her secret, but the use of harming Chloe with a dog pill was a strategy that the film deployed for shock value.
Run's ending reveals that Diane lost her own baby years ago. She was so distraught that she ended up stealing another one from the hospital that was born the same day — that baby ended up being Chloe. In the aftermath, Diane pumped Chloe full of pills for her entire life, causing various illnesses to surface that work to ensure Chloe will never leave her. Diane, who likely has Munchausen syndrome by proxy, convinced herself she was saving Chloe, so she spun a complicated web of lies to back up her delusion. Since the pill she settled on to cause Chloe's paralysis was intended for a dog, Diane had to invent a reason for needing it — hence a family dog. Diane hints that she doesn't have much of a social life, meaning that no one probably ever came to her house. That meant no one could dispute her claim of having a dog, although it is curious how she'd get the medication without ever having seen a vet directly to diagnose the non-existent pet.
Chloe's investigation into the identity of that pill took up the first act of Run, so the reveal that it was actually meant for a dog highlighted the cruelty of Chloe's situation. Diane presented herself as a loving mother, but she was willing to feed her daughter pills meant for an animal. It's a highly shocking reveal for the audience. The dog pill was the first hint that something wasn't right in Run, and while the movie never further detailed how Diane was able to acquire this medication, the meaning behind her actions was ultimately more important to the movie's narrative.