Desdemona and Emilia are both abused by Iago in Othello. Iago abuses Desdemona by using manipulations and lies to convince Othello that she is cheating on him with Cassio. Iago knows Desdemona is innocent but is willing to use her ruthlessly to achieve his goal of destroying Othello's life.
Iago also knows how loyal Emilia is towards Desdemona. Nevertheless, he bullies her into giving him the handkerchief that Othello gave to Desdemona as a special remembrance of his mother's life. Iago abuses his wife's trust because he does not tell her he plans to use the handkerchief to hurt Desdemona by framing her as an adulterer. Iago is indifferent to the deep pain it will cause Emilia when she finds out she played an unwitting part in harming her friend and mistress.
Desdemona is also abused by Othello, who takes out on her his fears that she is being unfaithful to him. He abuses her not only with harsh words and violence, but by not sitting down and discussing with her exactly what is going on. When he is wrongly convinced she has cheated on him, he kills her, the ultimate form of abuse.
Shakespeare shows a patriarchal society where men are too quick to suspect women of sexual infidelity and also to use them for their own purposes.