In the case of my mother, who lived in a different state with family that hates me and my sister... From her boss, who had my sister's number from some recent situation. Wouldn't have found out for ages if it hadn't been for that. Sometimes I wonder what that would have been like, but I'm glad I don't know.
If you don't already, make sure at least one person close to your family/friends that you'd want to know about has your number and knows to get in touch.
The authorities often go with address if they don't have any other clues. When my mom died, she lived with her sister, who hates me and my sister... We found out by chance because my mom's boss reached out to offer condolences, and then we had to call the coroner to let them know she had living kids. Her sister hadn't revealed our existence.