Can a foreign company hire employees in Israel without registering locally?

Not safely. If a foreign company employs Israeli residents who work in Israel, it will generally be considered to have a permanent establishment in Israel and must register with the Israel Tax Authority and National Insurance Institute, withhold income tax and social security contributions, and comply with all Israeli labor laws. Operating through a local employer of record (EOR) or establishing an Israeli subsidiary or branch is the correct approach. Paying employees informally or through a foreign payroll creates significant legal and tax exposure.