"The food is welcomed by the elephants."
Because 'willkommen sein' is a compound verb. In this case, you put the auxilary where the verb should be and put the actual verb to the end of the sentence, hence you get 'ist ... willkommen'.
Why is it wrong to add a dative preposition to this sentence? I wrote: "Das Essen ist VON den Elefanten willkommen." Does that not say the same thing?
"to welcome" in English is a verb. "willkommen" in German is an adjective that is used together with "sein" to make the compound 'jemandem willkommen sein'. You can't treat 'willkommen' by itself as a verb. The expression only works as a whole.
First, is "Das Essen" because food is neutral. Second, in German, as explained above when you used a compound verb such as "willkommen sein" you use the verb (sein) in the second position of the sentence (verbs always go in second position, even if the subject is after it), and the other part at the end of the sentence (willkommen), so you don't need to use bei; finally in the dative deklination plural uses "den" (masculin uses "dem", neutrum uses "dem" and feminin uses "der"), you can't use beim (bei dem) because is not masculine.