Livingstone was deemed a high-risk offender and was subject to an Electronic Supervision Order that dictated he must wear a GPS-tracking ankle bracelet at all times.
Southland police were last night hunting Michael George Mulligan, 30, who was on electronically monitored bail and facing driving and domestic violence charges when he removed his monitoring bracelet.
Police say he should not be approached but it is understood he is not deemed "high risk".
The changes came into effect on Wednesday after urgent discussions between Corrections and police.
Corrections Minister Sam Lotu-Iiga said the response time in the Livingstone case was "unacceptable".
"I asked Corrections to work with police to speed up responses to EM breaches by high-risk offenders and they have reassured me that these measures have been taken."
There are 3700 offenders being electronically monitored on community sentences like home detention, and another 400 alleged offenders on EM bail.
Those sentenced are managed by Corrections and those on bail by police. However Corrections carry out all monitoring through private security company 3M and their partner First Security.
The two agencies went through the total 4100 people being monitored, identified those who were the "highest risk" and produced a list of about 160 names, based on a combination of factors including sentence type, type of offending, risk of reoffending and a variety of static and dynamic risk factors.
If tamper alerts are received for anyone on that list, 3M will immediately contact Corrections national EM Response Team. That team will then decide what action to take "to ensure the swiftest and most effective response".
"This may include immediately notifying police for an urgent response, dispatching a contracted field officer, and/or making contact with the offender directly," Corrections national commissioner Jeremy Lightfoot said. "This replaces the previous practice [of] dispatching a field officer to the offender's residence and awaiting an outcome before contacting Corrections or police."
Electronic monitoring
•Corrections electronically monitors 4100 people through security companies 3M and First Security
•Of those, 3700 are sentenced prisoners subject to community sentences like home detention or post-sentence supervision orders that dictate GPS monitoring. Those people are managed by Corrections.
•The rest are before the courts and have been released on electronically monitored bail. Police manage these cases but Corrections carry out the monitoring.