Can an immigrant who was detained and signed the papers to be deported, change his/ her mind?

My aunt and her husban have been living in the US for more than twenty years. They have no criminal background, have payed taxes and have followed all of the US laws while in this country. One of her co workers wanted her fired from he job so that her daughter could work ther because it was a family owned bussiness. She would treat my aunt very badly and threatened to call immigration on her, and she did because she knew where she lived and everything. well my aunt and her husband were detained and they both signed the papers nstating that they accepted to wbe deported and did not want to fight for their case. well, my aunts boss said that he will pay for their lawyer abd cover all charges, except that my aunt already signed the papers. can she change her mind, and can the papers she signed be annled or something?