Fall detection

If you can't have the phone at least in bluetooth range of the watch then you would need the cellular version of the watch.

Use fall detection with Apple Watch

P.S.

For family sharing you will also need a cellular watch;

What you need

• An Apple Watch Series 4 or later with cellular, or Apple Watch SE with cellular, with watchOS 7 or later.
• An iPhone 6s or later with iOS 14 or later for the initial watch setup.
• An Apple ID for yourself and one for the family member who will use the Apple Watch. Your Apple ID needs to have two-factor authentication turned on.
• A Family Sharing setup that includes the person who'll use the Apple Watch. You need to have the role of organiser or parent/guardian to set up an Apple Watch for a family member.