I'm sure there is a device out there on the market, but I'm not having any luck with google/amazon.

I have a family member who is an avid runner, but may be dealing with some memory issues. Nothing diagnosed yet, but family is slightly concerned. He won't carry a cell phone while running, so I'm researching to see if there is some small device that could be helpful in locating him if he has an issue.

What watch does the runner use and are you willing to spend the money to upgrade?

There are LTE Garmin, Apple, etc. watches out there. I know Garmin has some that will send messages/emails to emergency contacts with a link to the run so they can track them.

I use a Garmin inreach mini. However if he doesn't run with a phone getting him to run with this will be the same issue.
The device itself is very compact, can send a sos at any time and ping location every 5-10 min depending on plan. To send texts via satellite you will need a phone to type the texts to send through the device. The plus side is that you can be in the middle of nowhere out of cell service.

inreach is the way to go, but yeah, if the person won't carry a phone...

Air tag won't really work without iPhones nearby to relay the location. I'd say Apple Watch and set it up so you can see the "Find My" location. My last race that was how my wife tracked me.

Is someone with memory issues going to remember to charge and wear an Apple Watch?

Watch location only works in cell coverage.

Wife bought me a Garmin 945LTE because I refused to run with a phone and would rarely carry it when cycling, either. For $5/mo, the LTE plan is pretty reasonable and the functionality has worked well on the couple occasions I've had to send the "I'm okay, but please come pick me up" message.

Garmin/Samsung/Apple watch may be our best option. Just didn't know if there was anything like a airtag that could be clipped to a shoelace or something that works on cell networks. Thanks for the info