It's called a Cancellation of Removal and there are criteria for it. For LPRs: Foremost is no aggravated felonies. I have written about the other requirements elsewhere on this site, which are basically an LPR for at least 5 years, including 7 years in any lawful status. INA sec. 240A(a)
For non-LPRs, interestingly there is no per se bar due to agg. felonies, but the excluded crimes are fairly extensive, plus 10 years physical presence in U.S., good moral character during that presence, and would result in unusual hardship to a citizen or LPR child, parent or spouse. INA sec. 240A(b)
For LPRs there is no defined hardship criteria, but since the relief is discretionary, attorneys argue the hardship angle anyway.
I seem to recall that your case was for an undocumented non-citizen. If he has been here ten years, then he may have a shot at 240A(b). But the main issue with him is whether or not his 3rd degree assault is removable or a bar to admission in the first place. If it is not, then if he adjusts he can stay. If it is a bar to admission and he does not adjust, he will be removed and there is no relief available to him.
For non-LPRs, interestingly there is no per se bar due to agg. felonies, but the excluded crimes are fairly extensive, plus 10 years physical presence in U.S., good moral character during that presence, and would result in unusual hardship to a citizen or LPR child, parent or spouse. INA sec. 240A(b)
For LPRs there is no defined hardship criteria, but since the relief is discretionary, attorneys argue the hardship angle anyway.
I seem to recall that your case was for an undocumented non-citizen. If he has been here ten years, then he may have a shot at 240A(b). But the main issue with him is whether or not his 3rd degree assault is removable or a bar to admission in the first place. If it is not, then if he adjusts he can stay. If it is a bar to admission and he does not adjust, he will be removed and there is no relief available to him.