About 25% of all immigrants are undocumented.
There is no paper trail for them.
There is no way to accurately describe the individuals in this group, because they are “unknown”.

According to their supporters, they use bogus names and social security numbers. They often work for cash.

When they live in HUD housing, with their legal resident relatives, no records exist, they are never counted. There are no statistics of any kind available, for illegal residents living in HUD housing.

When illegal residents live with legal residents receiving food stamps, they must be listed on the application. They do not “receive benefits”, as an additional household member, but they eat the food purchased with the food stamps. Illegal residents receive the nutritional benefit of good stamps. There is no statistical information available.

Statistically speaking, illegal immigrants are invisible, do not exist (except in the census count).

On the other hand, legal immigrants are well documented. All kinds of paper trails to chart them as individuals.

Of non-citizens in Census Bureau data, roughly half are in the country illegally.
In 2014, 63 percent of households headed by a non-citizen reported that they used at least one welfare program, compared to 35 percent of native-headed households.
Compared to native households, non-citizen households have much higher use of food programs (45 percent vs. 21 percent for natives) and Medicaid (50 percent vs. 23 percent for natives).

While most new legal immigrants (green card holders) are barred from most welfare programs, as are illegal immigrants and temporary visitors, these provisions have only a modest impact on non-citizen household use rates because: 1) most legal immigrants have been in the country long enough to qualify; 2) the bar does not apply to all programs, nor does it always apply to non-citizen children; 3) some states provide welfare to new immigrants on their own; and, most importantly, 4) non-citizens (including illegal immigrants) can receive benefits on behalf of their U.S.-born children who are awarded U.S. citizenship and full welfare eligibility at birth. 63% of Non-Citizen Households Access Welfare Programs | Center for Immigration Studies

Legal immigrants are required to show how they will be supported, without welfare, to maintain legal status (for the first five years). In general, they are educated and self supporting.

Illegal immigrants often start benefitting from the welfare system from the first day they are in the country. They are generally uneducated, with little or no job skills. We are told this is their strong point, they will take jobs no normal person would want.

Statistics that show immigrants as a benefit to society only consider the legal resident immigrants. There are no reliable statistics for the illegal residents.