It's kind of a silly sentence, but I was wondering how you would get the で particle's meaning into a modified noun. Like you could say 'フォークで食べる' but how could you turn that into a noun? I hope this makes sense.
Generally, で is not used like フォークは食べるための道具. If you want to use で no matter what, you can say フォークはそれで食べるための道具, but it is wordy.
Nouns marked by the particle で (of means) can be relativized, but saying
I think would be too ambiguous. People would think "A fork is a tool you eat."
To disambiguate, you can explicitly include an object:
フォークはものを食べる道具です。 A fork is tool you eat things with.