Well, usually, there are 2 types of reaction on a constructive feedback: positive and negative. It depends on a person you are talking to, as well as from the form, in which the feedback is given. Here is a good essay on a correct way to give a negative feedback: https://studentshare.net/management/88118-feedback.
Still, even if feedback is given correctly, a person might be offended. It depends on loads of other factors, like complexes, fears and overall personal psychology of a person. The situation, also, can be vice versa: the feedback will be given poorly, but the person will make good conclusions and improve his/her work.