How do I find a missing person in Las Vegas?

My mother has not been heard from in several weeks by anyone. This is very unlike her. She is a vagrant who has been roaming shelters and acquaintancs who let her sleep under their roof. For years she has done this. Any time she had phone issues, she would use the library's computer to reach out. No method has worked. Everything goes unanswered or left unread. There has been no reason for her to cut contact.

She always promised us that she would keep our contact information on her (her purse) and that several of her close friends know my/our number.

I can feel it in my bones that she is dead. If she died and something happened to her purse, the police couldn't contact us.

How do I find her? I looked up the morgue's unclaimed people but that is really out of date. I know a general area of the last zone she would frequent but who knows where she went off to.

The entire family does not live near Las Vegas. How can I do this via phone? Should I hire a private investigator or fly into town?

Are there organizations, that aren't false efforts, that can go through the Jane Does?

Please help me find my mom...