As with any visa applicant, non-citizens applying for U visas to the U.S. or for adjustment of status must prove that they are not "inadmissible." The main grounds of inadmissibility have to to do with issues like past criminal convictions and immigration violations, as well as a few health grounds. Another ground of inadmissibility that causes trouble for many visa applicants is likelihood of becoming a "public charge" -- that is, likelihood of receiving government assistance based on financial need.
The public charge ground of inadmissibility has, however, been removed as an obstacle for U visa applicants. This is as a result of a law known as "VAWA 2013," which says that the “public charge” ground of inadmissibility at INA § 212(a)(4) does not apply to a noncitizen petitioning for or who has been granted U nonimmigrant status. This also applies to derivative family members of U visa applicants.
Therefore, if you are seeking or have been granted principal or derivative U nonimmigrant status, you need not be concerned about the public charge ground of inadmissibility, and need not submit a waiver application if you are low-income and have received or might receive means-based government assistance. In line with this, the public charge ground of inadmissibility will not be considered if and when you apply for a green card (adjustment of status)
As of August, 2014, the U visa application form (Form I-918) still asks about whether you have "received public assistance in the United States from any source." If you are filling out this form now and encounter this, you should write in “not applicable” in response. USCIS intends to remove this question in the next new version of the form.