Sorry, I am not sure what you intend to hear. I try to express my(!) understanding of it here. I have little proof for it (not finding the expression "to become offended" but "to be offended" in dictionaries is not a proof).

With "to be offended" I would describe two cases

• the state of mind of a person that is "offended" and

• the passive form of "offend", i.e. the action to move somebody else into that state,

while "becoming offended" is the process of a person who will finally reach the state "offended" (I intenionally used the gerund). "Becoming" describes a change of state of someone, not the action of somebody else that one has to suffer.

I try an example:

He is trying to offend her and, indeed, she starts becoming offended. Being offended makes her angry, too.