Many forms of Relief exist to win a Removal Proceeding
A person who is found inadmissible or deportable may have several forms of relief available to him or her. These forms of relief include cancellation of removal for certain lawful permanent residents, including relief under former INA § 212(c), cancellation of removal or suspension of deportation for certain non-permanent resident aliens, cancellation of removal under the Nicaraguan Adjustment and Central American Relief Act (NACARA), adjustment of status, political asylum and/or withholding of removal, nunc pro tunc permission to reapply for admission after removal, deferred action, certain waivers of inadmissibility, and private legislation.
A lawful permanent resident who is inadmissible or deportable is eligible for relief from removal if he or she has been an alien lawfully admitted for permanent residence for not less than five years, has resided in the United States continuously for seven years after having been admitted in any status, and has not been convicted of an aggravated felony
NACARA guaranteed continued relief from deportation under former INA § 244(a), in effect before the enactment date of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996, for certain Salvadorans, Guatemalans, Eastern Europeans and persons who were applicants for suspension of deportation prior to April 1, 1997, and who were not served with an order to show cause or committed certain crimes prior to being physically present in the United States for a period of seven or 10 years.
Certain aliens who are not deportable as aggravated felons or terrorists are eligible to leave the United States voluntarily at their own expense in lieu of being subject to removal proceedings depending upon certain circumstances
The burden of proof to establish eligibility for relief from removal is on the applicant. Persons applying for voluntary departure and for cancellation of removal for non-lawful permanent residents must also show good moral character for the requisite period of time required for the relief requested
There are several forms of relief related to asylum. This would be the defensive asylum application, withholding of removal and/or CATS - or Convention Against Torture.
Normally, Asylum would be the best form of relief, but if one cannot get that, they can certainly try for the other forms.