In each of the break-ins, which started in March, the families' addresses were listed in newspaper obituaries, police said.
Officers conducting surveillance caught the woman last Friday in the act of burgling a home which had been mentioned in an obituary, said police spokesman Jan Schabacker. The authorities continue to investigate.
"Survivors can protect against such events, by avoiding naming the addresses of those in mourning in obituaries," Schabacker said in a statement.
He also said that homes should be monitored by someone trustworthy when they are empty and families should always avoid keeping large amounts of jewellery or cash at home.