Stop Illegal Reentry Act

What H.R. 749 does, in plain terms

Stop Illegal Reentry Act This bill increases criminal penalties for certain non-U.S. nationals (aliens under federal law) who illegally reenter the United States after removal or exclusion. Generally, an individual who had been denied entry into or removed from the United States and who later enters or attempts to enter the United States without prior approval from the Department of Homeland Security shall be fined, imprisoned for up to five years, or both. Current law requires a fine, imprisonment for up to two years, or both, for such an individual. An individual who had been denied entry or removed three or more times and who later enters or attempts to enter the United States shall be fined, imprisoned for up to 10 years, or both. An individual who was convicted of an aggravated felony or convicted at least two times before removal or departure and who subsequently enters or tries to enter the United States shall be imprisoned at least 5 years and for up to 20 years and may also be fined. Currently, there is no minimum term of imprisonment for an individual who reenters after a conviction for an aggravated felony, and there are no criminal penalties for a reentering individual who had been convicted at least two times (other than the penalties for illegal reentry generally).

Official summary by the Congressional Research Service, via Congress.gov.