Below is a shortlist of some useful sites for finding Diur Mugan - דיור מוגן - Independent Living Facility options in Israel. The best current starting points are the government search page, the Israeli Protected Housing Residents Association directory, and a few commercial/index sites that include phone numbers and addresses.
Gov.il protected housing search (Hebrew) - official government search page for בתי דיור מוגן; however, the page itself notes that licensing regulations are still pending, so it should be treated as an official listing source, not a full quality-certification tool.
Israeli Protected Housing Residents Association – Find a Home (Hebrew) - lists 46 member homes across the north, center, and south.
Diur Mugan B’Click - commercial directory-style results page with many facility names, addresses, and phone numbers.
Israel Retirement Homes Database - English-facing database with named facilities and phone numbers, useful for Anglos even though it is not limited strictly to Diur Mugan and hasn’t been updated in a few years
Semerenko Group directory - English-oriented directory/guide for Diur Mugan in Israel, though it is advisory/commercial rather than official.
Directory + guide for English-speaking retirees - more of a guide than a registry, but useful for English-language orientation.
Please note: Please note that this is not a complete list of all options!