Connecting verbs without the preposition "to"
Solution 1:
In this case, Krashen claims, and "the type of environment" fosters. It looks clunky when you pull just the verbs out of it for analysis, but the "second verb in the infinitive" is not a hard and fast rule, it's just how it often shakes out. It might have been more clearly worded with a modal verb like "can", i.e., "claims can foster", but the verbs in this case correspond to two separable subjects.