The expression 'reduced to' can be followed by a noun phrase; an illustration is 'he was reduced to a quivering wreck'. In this sentence, quivering is an adjective and wreck is a noun.
The verb form "-ing" can act as a noun; this explains the use of the word "asking" in your example.
It can also be considered that "to" is a preposition in your example. Prepositions are followed by the "-ing" form; as in by doing, after saying.