I need some suggestions for keeping a wanderer safe in the house. Any ideas?

This was my attempt at preventing my wife from wandering: After she left the house at 2 AM on a snowy, cold, winter morning, I decided to install a double keyed lock on the front door. (BTW, I found her by following her footsteps in the snow). I didn't use any bells or alarms because I thought those were all after the fact, she was already up and moving. A new lock that had to be opened from the inside with a key that I kept, I thought whould work. Although she had dementia, she was resourceful. She went out the window! I wound up securing the windows also, but thought that this is becoming dangerous for the both of us. That episode was a significant reason for my looking for a new home for her. You're already sleeping on the couch with one eye open, and fearful of leaving her alone. You can't count on the neighbors finding her at 2 AM. The search for a care facility is in both your and your mom's best interest.

You deadbolt the door AND put a hook and eye latch at the far top of the door so that it can not be reached by her.
I had the same problem and I actually had a keyed inside deadbolt. So that a key had to be used to open the door. I wore keys around my neck for 4 years 24/7.
There was a program in the County where I live called CareTrack and the county Health Department fitted my Husband with a device that looked like a watch. information and a photo was taken on my Husband and if he wandered off I was to call the police and tell them he was on the program. They came and set up like a little command station at the end of my driveway and they got out the book, got his "signal" information then an officer rode around with an antenna that would pick up the signal.
There are other devices that can be fitted in a shoe, on a bracelet. Or depending on if the person carries a cellphone you can find a person that way.
PLEASE let the Fire Department and the Police Department know that you have a vulnerable person that wanders so that if you have to call them they can respond fast. (you do not have to wait 24 hours.)
You can not leave her alone.
If you can not get caregivers to help you might have to consider the option of placing her in Memory Care.

I put Christmas doorbell hangers with bells on her bedroom doorknob, bathroom doorknob, front doorknob, and back doorknob. Every time I heard the bells, I knew she was wandering in the evening. To avoid her going to the bathroom in the evenings alone I put a portal toilet in her bedroom. Again, the Trazadone and Sertraline will resolve the wandering around which will make your job in caring for her much easier.

My mom was doing these types of things 3 years ago. The doctors but my mom on Trazadone 50mg and Sertraline 50mg. I cannot tell you how much those 2 drugs helped my mom with all her issues. In addition, I hide my mom’s slippers and shoes from her once I put her to bed in the evenings. My mom would never go outside barefoot. Hide her shoes and slippers to avoid her from wandering outside.

My mother lived with me for nine months after she broke her hip, and I had to sleep on an inflatable mattress on the floor next to her to keep her from falling.

She was much happier when she moved into residential care, and although I slept better, I’d already gained 60+ pounds of stress weight.

Lock her in her room at night. You keep the key to the door.
Install locks on the doors that only unlock with a key or a numerical combination.

Some people have luck installing a simple slide lock or hook at the top of the door, also put alarms on the door so you know if they've been breached. Also contact your local law enforcement, many of them keep a database of people with dementia and some even provide a gps bracelet, if yours doesn't consider getting one of your own.