Be good
Be given
Be understood
Be devoted to
More resources are devoted to the care of refugees.
Be is the first verb here.
They requested for more resources to be devoted to the care of refugees.
Be is not the first verb now. Requested is the first verb. The second verb is in the infinitive usually with (to) be.
In this case the relative pronoun that is not a true pronoun. Here it has the same meaning as (for) and is a part of a preposition. Normally verbs inside prepositions are either in their noun form by adding (ing) or they are in their infinitive form. (Be).
There maybe another rule you learned though. This is just my native opinion.