When I was thinking about the saying, 'the dose makes the poison,' I ended up remembering a show I didn't pay close attention to, but I was around for the Twilight Zone Twist at the end. I was pretty sure it was a more mundane episode of The Twilight Zone, but I couldn't find it on a list of episode summaries.
A married couple are taking care of an elderly mother (I think it might have been the wife's mother, but I'm not sure), but for money-related reasons like life insurance or expensive medical bills, they decide to kill her, and settle on poisoning her tea for the method. It takes far longer than they expected for her to die, so they increase the dose. After she does finally die, the family doctor makes a comment about her heart condition, and how she needed treatment by a certain drug, commenting on its reputation as a deadly poison, yet for someone with her condition, it's life-saving medicine at the right dose. Naturally, the drug in question was what they were giving her, unintentionally medicating her and extending her life instead of shortening it.