“Withholding-only-proceedings” refers to one of the several types of proceedings (hearings) existing in the USA (twelve different types, according to one of the links below) dealing with immigration issues and conducted before immigration courts.

In this context it is important to mention section 240 of the Immigration and Nationality Act (INA), which sets forth the meaning of the term “removable” and the expression “removal proceedings” concerning foreign citizens (= “aliens” in the immigration terminology). According to the US immigration legislation, particularly the INA, some aliens are not entitled to proceedings under § (= section) 240 of this Act. Such aliens are however entitled to withholding-only proceedings. In the “formal” removal proceedings under section 240, the alien in question can respond to pleadings and may pursue relief from removal from the country in several different ways. Basically, proceedings under section 240 offer a higher degree of procedural protections, including greater administrative and judicial review than the rest of proceedings. This is NOT the case of “withholding-only proceedings” and here lies the main difference with the “normal” situation (§ 240).

See here:
https://www.justice.gov/sites/default/files/eoir/legacy/2014...
U.S. Department of Justice Executive Office for Immigration Review Office of the Chief Immigration Judge
(…)
C. TYPES OF IMMIGRATION HEARINGS
There are twelve principal types of immigration proceedings conducted by the Immigration Court: removal, deportation, bond redetermination, asylum-only, credible fear, exclusion, withholding-only, reasonable fear, claimed status review, NACARA-only, rescission and continued detention review. All the proceedings involve an alien referred to as either a respondent or an applicant, whom the DHS [stands for Department of Homeland Security] has charged with violating the immigration laws of the United States.
(…)
7. Withholding-Only Hearing
Certain aliens are not entitled to proceedings under § 240 of the Act, yet these aliens are entitled to withholding-only hearings before an immigration judge. If an alien who is not entitled to a proceeding under § 240 of the Act requests asylum, the DHS will file a Form 1-863, Notice of Referral to Immigration Judge, with the immigration court. Withholding-only hearings are very similar to asylum-only hearings except that aliens eligible for withholding-only hearings have previously been ordered removed (administratively) by the DHS or the DHS has reinstated a prior exclusion, deportation or removal order.

As it can be seen, the matter is extremely technical and complex in itself.

Translation: Some important words about the translation. I have found the rendering “retención” for “withholding” on several web sites of international organizations and also on US sites, but I have to say that “retención” does not convince me (¿retener una deportación?), it simply sounds weird to my Spanish (European) ears, and this is the reason why I suggest “suspension” instead of “retención” for “withholding”. Certainly, “withhold” translates into Spanish as “retener” (and “withholding” as “retención”), but also as “detener” (= “suspender”), the rendering I deem most accurate in this case.

A final remark: Juan, with all due respect, due to the extreme complexity of this query, I am convinced that it should not have been asked in the first-validated-answer mode. This type of questions requires reflexion, time and patience both for asker and answerers. The first-validated-answer mode is not appropriate in this case.


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Note added at 4 hrs (2020-10-07 23:16:36 GMT)
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From the Immigration and Nationality Act (2011), section 240:

http://www.lawandsoftware.com/ina/INA-240-sec1229a.html
TITLE II: IMMIGRATION Part IV
Inspection, Apprehension, Examination, Exclusion, and Removal
§ 240 (8 USC 1229a) Removal proceedings
a. Proceeding
1. In general
An immigration judge shall conduct proceedings for deciding the inadmissibility or deportability of an alien.
2. Charges
An alien placed in proceedings under this section may be charged with any applicable ground of inadmissibility under section 212(a) of this Act [8 U.S.C 1182(a)] or any applicable ground of deportability under section 237(a) of this Act [8 U.S.C 1227(a)] .
3. Exclusive procedures
Unless otherwise specified in this chapter, a proceeding under this section shall be the sole and exclusive procedure for determining whether an alien may be admitted to the United States or, if the alien has been so admitted, removed from the United States. Nothing in this section shall affect proceedings conducted pursuant to section 238 of this Act [8 U.S.C 1228] .


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Note added at 5 hrs (2020-10-07 23:28:25 GMT)
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You will find here the translation “retención de la remoción”, which I do not consider satisfactory. However, this link is insofar interesting as it explains the distinction between “asylum-only” and “withholding-only proceedings”.

http://www.nosapo.com/terminos-importantes
Retención de la remoción (Withholding of Removal)
Esta orden emitida por un juez de inmigración que, como el asilo, protege a una persona de ser deportada a un país donde temen ser perseguidos, lo que demuestra más de un 50% de probabilidad de ser perseguidos en su país de origen por su raza, religión, nacionalidad, pertenencia a un grupo social particular u opinión política. Las solicitudes de retención de remoción se realizan en el mismo formulario que las solicitudes de asilo (formulario I-589) y también se realizan simultáneamente con la solicitud de asilo. Sin embargo, si bien un oficial de asilo o un juez de inmigración pueden otorgar asilo, solo un juez de inmigración que escucha un caso para alguien en proceso de deportación puede otorgar la retención de la expulsión.
(Por cómo la retención de expulsión difiere del asilo: nota al pie de página, 5)

Las opciones que encontré.
Espero poder ayudar en la búsqueda.
Dejo a continuación algunos de los enlaces consultados:
https://www.uscis.gov/es/programas-humanitarios/refugiados-y...
https://pennstatelaw.psu.edu/sites/default/files/Self Help G...
https://www.unhcr.org/en-us/asilo-defensivo.html
https://pennstatelaw.psu.edu/sites/default/files/documents/p...
https://www.uscis.gov/es/i-589