I wouldn't really see that as an exploit, unless you urged your poor sim to participate in a particularly dangerous activity for the purposes of killing them to raise the value of paintings lol.
Deathflowers are used automatically. However, in the PC version, this only buys an elderly sim a couple of days at the most unless you see to their aging before Grim stops by again. It's possible that in the console version that Deathflowers just don't save sims from death by natural causes. However, I've never played the console version so this is only a theory.
Death by old age is the final age transition of a sim (a birthday of sorts). It could be possible that the game decided that "today is this sim's last birthday," and aged them up at the appropriate time, even though you had reduced their age prior to that.