It would be grammatically correct, but the sentence would have an unusual meaning: why would they get the worst possible produce?

Instead, you can say

Ils vendent les légumes les plus mauvais qui soient.

Qui soi(ent) = that exist, existing in the world, qui exist(ent).

Un peu comme l’usage de “ever” en Anglais, on a un renforcement du sens:

It’s the worst book. It’s the worst book ever.

Je lui donne les plus beaux légumes.
Je lui donne les plus beaux légumes qui soient.

On a en plus du renforcement de sens, une certaine amélioration “esthétique” de la phrase. Elle est un peu plus littéraire que si on avait ajouté “du monde”, ou autre.

“qui soit” / “qui soient” = “that exist(s)”

It’s basically the same usage as “ever”. The full phrase corresponding to “ever” would be something like “that has/have ever existed”, like:

They are selling the worst vegetables that have ever been grown.

In French, the full phrase would be “qui aient jamais existé”, such as:

Ils vendent les pires légumes qui aient jamais existé.

Note that “jamais” is usually translated by “never” when talking about a frequency, but this is also the right way to translate “ever”.