Hundreds turned out for a public hearing on proposed changes to Santa Clara County’s sanctuary policy Tuesday, as the slaying of a local woman stirred emotional debate over how police should handle the release of immigrants with serious or violent criminal records.

After a marathon seven-hour meeting, the Santa Clara County Board of Supervisors voted 4-1 to explore potential amendments to the county’s sanctuary policy following the slaying of 59-year-old Bambi Larson, who was stabbed in her South San Jose home, allegedly by an undocumented immigrant.

The vote does not immediately change the current policy but gives officials an opportunity to discuss potential changes down the line. County staff and law enforcement will have 60 days to study how law enforcement agencies may notify U.S. Immigration and Customs Enforcement when individuals convicted of serious or violent crimes are released from their jails.

Supervisor Susan Ellenberg, the lone dissenter, said she didn’t feel it was necessary to re-evaluate a policy that is already working and was concerned it would drain county resources.

Politicians and local law enforcement officials — frustrated with a county policy that says police should not notify federal immigration authorities when an undocumented immigrant is released from jail — had called on county leadership to loosen these restrictions in order to apprehend violent criminals like the man accused of killing Larson.

Larson’s supporters — who blamed her death on the county’s restrictive sanctuary policy and said it “harbored” undocumented immigrants — asked the board to allow law enforcement to notify ICE when a violent criminal is released into the public. But they were outnumbered by immigration advocates who argued that amending the policy would promote discrimination against immigrants, violate their due process rights and play into President Trump’s “mass deportation” policies.

One man, a rabbi, said changing the policy would mean, “scapegoating an entire group because of the actions of one.”

“You can’t be pro-ICE and be an ally of my community,” said Katiuska Pimentel Vargas, an undocumented San Jose resident and immigration activist.

Larson’s death has become a focal point of the debate on local sanctuary policies, which sometimes offer more protections than SB54, the state’s sanctuary law.

Following Larson’s killing, police have criticized the county policy requiring them to ignore requests by ICE to hold inmates past their release dates until they’re picked up by immigration officials. The state’s sanctuary law, known as the California Values Act, also prohibits police cooperation with ICE, with the exception of undocumented immigrants who have committed serious or violent felonies.

One woman, who did not want to be identified Tuesday, said the county should be deporting undocumented immigrants who are violent criminals.

“Bambi Larson’s children will never see her again. Her grandchildren will never see her again,” she said. “We take a backseat to people who are here illegally.”

The proposal approved Tuesday, presented by Supervisors David Cortese and Mike Wasserman, would tap county officials to work with law enforcement agencies and community leaders to craft policy amendments in which ICE would be notified of inmates convicted of violent felonies or other serious crimes and have sufficient time to obtain arrest warrants before a serious offender is released from jail. It would also improve the release process for mentally ill inmates in danger of harming themselves or others.

“I’m in favor of removing individuals who have committed serious and violent crimes from our communities whenever and however possible,” said Wasserman. “I understand the fear in the community. And that’s why my referral today is so specific, so targeted.”

Carlos Eduardo Arevalo-Carranza, 24, an undocumented immigrant from El Salvador, is charged with stabbing Larson to death in her San Jose home. Arevalo-Carranza, whom San Jose Police Chief Eddie Garcia called a transient and “self-admitted gang member,” was convicted of more than 10 crimes in the past three years, including burglary, battery of an officer, prowling and trespassing, and possession of methamphetamine. Yet he evaded immigration authorities in Los Angeles and Santa Clara County who sought to detain him several times.

Others said social issues in this case — among them mental health, addiction and homelessness — have gone ignored and should be addressed to prevent future tragedies.

Tatiana Sanchez is a San Francisco Chronicle staff writer. Email: tatiana.sanchez@sfchronicle.com Twitter: @TatianaYSanchez