My mother is obsessed with her purse. She has a death grip on it and sleeps with it. Any suggestions?

I think purse-clutching is pretty common throughout Little Old Lady Land, isn't it? Like tissues in the sleeves and covering everything in clingfilm and going "oof" when you get up.

I think the tummy bag is a great idea; but if she won't hear of swapping her established purse maybe you could feed a belt through it and keep it close to her that way?

Also... how long has she had this particular model? Because before you throw it out, make sure it doesn't in fact contain her eternity ring inside a tissue, inside said cling film, inside a folded brown envelope, deep inside the zipped compartment.

I wouldn't worry about it
In fact having a purse with fake money helped mom greatly during her first year in memory care - I had swapped out her normal purse for a smaller nylon cross body bag

She would spend hours going through it - counting her money and eating the little treats I would put in it - life savers and peppermint candies, a pack of cookies and the like
It was large enough to hold a readers digest

She too would sleep with it under her covers

CM in old lady land where I currently reside the purse is just like a small child's favorite
soft stuffed animal or "blankie" One daughter had a tatered teddy the other a mouse and my son much loved panda. I had a teddy and a donkey called " Docky"
To the elderly they are frequently their only procession that they can retain control over.
Let her keep her bag. Maybe empty the used toilet paper from time to time but it is her security and so valuable that someone is sure to want to steal it.
No in case anyone is wondering I don't store used toilet tissue but i do keep my purse handy becase that way i have my check book to pay bills , my book with phone #s and appointment book to write my many appointments.
My walker has a couple of canvas bags on it plus I have rigged up a wire basket so I can transport my meals and drinks. The basket is also useful for getting groceries into the house and transporting laundry.
Until you enter old lady land you do not understand why old ladies have certain behaviors. Hubby never moves without his computer and phone. you can usually find a milky way in his car.

I checked your profile, thinking your mom must have dementia, but it said age related decline.

This is a very common behavior in dementia. My mom also had a death grip on her purse. She ate with it in her lap. She slept with it under the covers. It had a long strap and she'd wear it across her body. I couldn't move it without her freaking out. There was nothing in it but a comb, lipstick and a mirror but you'd think she had $1000. inside.
She was like that until she progressed to the end of stage 6 Alzheimer's.
She seems to have "forgotten" about it and sleeps a lot now.

Have you seen other signs that her thinking and behavior is off?
Has she had an appointment with her doctor recently?

With dementia there is no changing their behavior and they can't understand that their behavior is unusual. Dementia victims can't process information and act on it.

I'd get her checked out by her doctor.

Allow Mom to have her purse.

Do you all remember Sophia on the Golden Girls? Carrying her purse everywhere was a running gag. I agree with the other posters about the tummy bag. If she still won’t relinquish the purse, let her keep it. I learned a long time ago when raising kids to “pick my battles”. As to Bingo Bucks, the residents of the nursing home where my parents reside give out real Bucks. They get a dollar for regular Bingo and $5 for a blackout. Bingo is serious business in the South. These senior citizens wanted nothing to do with fake money!

Veronica I know only too well how close I am to LOL Land.

Just recently, I have noticed a subtle change in my routine. I get dressed, I put on any make up I can be bothered with, I put on my scent, I put in my earrings... and as I stand up, I whip a Kleenex from the box and tuck into my sleeve.

Doomed!

My mom lived in a rural area. She heard a story through her friends that there was a vacuum cleaner sales team in the area. Supposedly they would go into a home where one would demonstrate the vacuum while the other pilfered the homeowners purse. (I’m not sure this actually happened).
She solved this problem. Should the team show up at her home, she had a “decoy” purse near her chair for the thieves. Being a frugal person who didn’t really want to give up anything, it didn’t really have much in it. The tissues. A pair of ankle hose. A comb. A church bulletin. It felt empty when picked up.
Her actual purse was hidden away in her bedroom. The decoy purse stayed in place so long that it was dusted along with other things in her sitting room.
MIL carried one of the big multi pocketed bags that was full of any and everything she might need. Very heavy. She would change her bag often to match her outfits. When she died a matching bag went into her coffin with many of the necessities packed inside.

Dear One, It is a comforting and soothing item much like the teddy or blanket we had as children and not uncommon. When my mother is agitated, her old purse with an expired driver’s license inside is her go to comfort and connection. It doesn’t harm her or anyone. Let her have it until she no longer wants it. Much love.

Get her a tummy bag. That way it can be with her all the time.
Amazon do a great one - 

amazon.co.uk/Unisex-Travel-Passport-Wallet-Festival/dp/B06WLN1Y96/ref=sr_1_5?ie=UTF8&qid=1522076125&sr=8-5&keywords=purse+bum+bag