If you get that unimaginable phone call in which you are informed that another woman was given your embryo by accident, and that she is now pregnant, shock is the number one emotion you will undoubtedly feel. The other woman, meanwhile, will feel similar. Legally, she will be under no obligation to continue the pregnancy, but she may do so, and this is something you can discuss together. And if you are the one who turns out to be pregnant, but with another woman's baby, you will have to make a very difficult decision. If you decide to carry the pregnancy to term, you will effectively play the role of a surprise surrogate mother.
Women who have had the wrong embryo implanted have no rights to keep the baby, understandably. Both parties will have ample opportunity to sue the hospital or fertility clinic, and the doctors whose error made a mix-up take place. But, as the story of two couples who faced a real life embryo mix-up (see how likely are embryo mix-ups to happen at your fertility clinic?) shows, it is much better to try and make sure that your fertility clinic has immaculate measures in place to prevent such tragedies from ever occurring. Asking many questions, and checking the clinic's track record, can assist you in this.