In French, we have this saying "Les carottes sont cuites", meaning "It's too late we can't do anything anymore" or "It's over for him" (He's dead) depending on the context.
The literal translation would be "The carrots are cooked", but I don't think it has a specific meaning in English.
I'm actually writing a short and silly story about how a fruit committed a hate crime on carrots, who are vegetables, and was planning to write this story in both English and French. If I can twist/find the goofy references on themselves the fruits would make in their dialogs in both languages, I have yet to find an expression in English that would mean "He is/They are dead" that would contain a vegetable reference, and it doesn't especially have to be carrots.
Best Answer
Although this isn't about vegetables specifically, I'm going to add it anyway—just so it doesn't get lost if comments are removed:
From Wiktionary's entry for goose is cooked:
My personal experience with this idiom is that it can not only imply just bad fortune, but also terminal fortune.
Of course, a more generalized idiom, which doesn't carry quite the same specific weight—and which also doesn't mention vegetables explicitly (but could still imply them), is out of the frying pan into the fire: