The Southborough Police Department’s failure to realize a convicted sex offender was violating a town law by living near a preschool for two years is reinvigorating a debate on whether residency restrictions are working.

“Nothing is foolproof,” said Carol Willoughby, a Southborough day-care center owner who in 2008 helped create the local bylaw that prohibits Level 2 and 3 sex offenders from living within 1,000 feet of areas where children or the disabled may congregate.