@Schipperke:
Yes, as Metro said, when Grim comes for a Sim who has a Deathflower in inventory, the Sim brings it out and gives it to Grim, who leaves happy and the lifestage is reset to the beginning. Grim won't show up again until the Sim dies again. If there's another Deathflower in inventory, the same thing will happen. No Deathflower and it's the end of your Sim.
All that being said, I'd suggest that you get another cook trained up as soon as possible anyway. It won't disqualify you, but the main point is to get your elders to qualify for Ambrosia. So, if it were me, I'd work toward that. But that's just me. Also, eating Life Fruit will extend your Sim's life by one day. If they eat, say 7 Life Fruits at once, they would get an extra week tacked onto their life. This can be another option until you have a cook who can make Ambrosia.