A person in removal proceedings is entitled to assert his/her right against self-incrimination under the Fifth Amendment due to any potential criminal charges arising from any admission of alienage, entry without inspection, or other factual matters alleged in the Notice to Appear. Matter of Sandoval, 17 I&N Dec. 70, 72, n.1 (BIA 1979).

Has your client carried his LPR card with him each and every moment since he became an LPR? If not, an admission to alienage on the stand would establish an essential element of an offense under 8 U.S.C. 304. Has he always filed a change of address within 10 days of moving? If not, admission of alienage under oath would establish an essential element of an offense under 8 U.S.C. 305. These are criminal offenses under the penalty provisions of 8 U.S.C. 306.

If an answer to the question might provide a link in the chain of evidence necessary to convict the client of a criminal offense under any of the following statutes, the claim of privilege should be sustained:

INA 266(a) and (b) " willful failure to register or provide change of address
INA 275 " improper entry
INA 276(a) " entering, attempting to enter, or being found in the US after removal

IJ or DHS cannot offer immunity " only the Attorney General can in writing.

Thanks to Bruce D. Nestor.