Some will. The rest will stay, get faux documents to get into the welfare system, or, there is always crime.
"The heavy use of welfare by working Mexican immigrants suggests that a guestworker program may create significant fiscal costs. Because the modern American economy offers very limited opportunities for workers with little education, it may simply not be possible to allow large numbers of unskilled people into the country without increasing the number of people using the nation’s welfare system. Of course, the guestworker program envisioned by some of its advocates would likely place severe restrictions on use of means-tested programs by the guestworkers. However, as we will see in the next section, although illegal aliens also are barred from using welfare programs, illegal aliens often make use of such programs, mainly by receiving benefits on behalf of their native-born children."
Excerpted from the following site CENTER FOR IMMIGRATIONS STUDIES
Those documents will not do them any good because they're not in the DHS database. Remember, the House bill mandates cross-checking all documents against the database before anyone is given a cent of governmnet money.
or, there is always crime.
That's what jails are for.
Another nice thing about the House bill is that it requires local law enforcement to check the immigration status of all arrested individuals.