The law of unintended consequences.

McALLEN — Illegal immigrants have started surrendering to local Border Patrol agents after crossing the Rio Grande, convinced they’ll be released by Immigration and Customs Enforcement, which recently turned hundreds of immigrants loose to save money.

In preparation for the sequester — federal spending cuts forced by Congress’ inability to reach a budget deal — ICE released several hundred low-risk illegal immigrants from detention centers last month and placed them on supervised released instead. The news reached illegal immigrants preparing to cross the border.

“These are people that are just voluntarily turning themselves in to our agents with the expectation they’ll be released,” said Border Patrol Agent Paul Perez, president of the Rio Grande Valley union of the National Border Patrol Council. “When you cross with the expectation that you’ll be released, there’s no need to hide, there’s no need to run. You just look for a uniformed agent and turn yourself in.”

ICE stopped releasing immigrants after the cost-cutting move sparked public outcry.

On March 3, many illegal immigrants detained at Border Patrol’s McAllen Station asked about being released, said agency spokesman Enrique Mendiola. Apparently, the illegal immigrants heard that ICE released detainees and wanted similar treatment.

“We make the arrests, we do the processing and then we hand them over,” Mendiola said, adding that Border Patrol doesn’t handle long-term detention — or release.