We now support fetching fulfillment data for criteria offers (collection and trait offers). You can see the updated documentation here.
Fulfillment is only supported for criteria offers placed using signed zone protection measures. Criteria offers placed without the signed zone are not eligible for fulfillment through the API.
The signatures provided for these criteria offers are tied to the fulfiller and consideration provided, and expire several blocks after they are generated. Fulfillment data is intended to be requested just before a fulfilling transaction is submitted, and shouldn't be cached indefinitely.