My mother has Alzheimer's, more on the severe case. She walked out of the house the other night and neither my father or I knew. Any suggestions?

Buy a bed side floor mat alarm.  Be sure to get one where the alarm sounds in your room or your fathers, if they don't share a room.  When your mom get's up and stands on the mat it will go off in the room where the alarm is.   It can run on batteries or you can also by an adaptor so you can plug it in.  I use both.  The alarm is portable so you can take it out to the living room and still know when she gets up.   There is a few second delay but it's nothing to worry about.  I bought mine on Amazon (approx. $178).  It has beveled edges.  Again be sure to get one that the alarm is in a different room and not the room where the mat is.
I've also heard if you put black mats in front of doors, they think it's a hole, due to depth perception being off, and they won't cross it.  Also, I heard a poster hanging on the door is a good deterrent. 
We put a double sided lock on the front screen door.  It has to be opened by a key to come in or go out.  I know some think its unsafe but its more unsafe if mom get's out and no one knows about it.  We keep a key hidden close buy.  This way she can still look outside but can't go out.  Hopefully some of these ideas help.  All my best.

When my friend, Beth, started to wander at night and needed 24 hour care, I hired an agency to provide that. But that cost $13,000 a month. I convinced her husband, Jim, that it was time to move to the memory care apartment I had found for them. That was about $10,000 a month for the two of them. I was lucky to have found a place that gives great care, pays attention to the needs of the people living there, and clues me in on their decline and what I should be ready for. The memory care floor is locked, of course, so no one can get in or out without a special fob to unlock a door. They had saved and invested enough money for me to do this as their POA for finances and medical care. Beth died after about 5 1/2 months there and her husband is still there in the same apartment almost 4 years later. He still receives good care and meals and is happy, except for missing his wife of 47 years. Each time I visit him, he reminds me that the only thing I have to do is live as long as he does. I always reply I am trying to do just that. They had no children or close relatives, so it was only a trusted friend who could play this role in their lives and we had been friends for over 40 years. We worshipped together, vacationed together and I worked in the same school with Beth for 18 years.
I am grateful for the guidance I have gotten in figuring out this care and that things went so well in taking on this responsibility.

All these answers are great. I have used them all. I also added door alarms that work great and I got them from a dollar store. I even had to put them on her window. I was afraid to use locks because she also started fires. I didn't want to not be able to get out fast if we had to. It was hard to do this by myself, so I alerted all my neighbors about Grandma. I went to each door, gave out pictures, phone number, and cookies, explained about her dementia and her escape issues. I just asked them to call me if they see walking down the street

For less $15 you can buy alarms that fit at the top of the doors and windows. When opened they sound off. You can put licks at the top of the doors too.

Yes, there are numerous! We used some cheapo ones that were magnetic (worked on doors and windows) and made a God-awful noise when the door/window was opened. Also, I put those little hook and eyes at the top of each door so it couldn't be opened. Learned this trick many years ago when raising twins, who were houdinis, and since my Mom was only 5 feet tall it worked for her too!

It seems like it’s time for a memory care unit. It’s not safe for her, not healthy for you.
I think people look at this whole situation so emotionally, they don’t really think it thru. Would they decide to operate on their loved one? Prescribe medication for them? Then why have them in an unsafe environment where they aren’t getting the professional level of care they need? You aren't putting them in jail, you are putting them in a facility that is particularly suited to care for someone with their particular problem. The staff is educated so they can best care for their needs. Not to be blunt but family aren’t most of the time.

I’m not a fan of the floor mat by her bed because she may need to get up for reasons other than walking out of the house during the night, I.e. use the bathroom, get a drink of water, etc. We decided to put a motion sensor just outside my dad’s bedroom doorway so he could be in his room without setting off alarms but if he leaves his room while we’re sleeping, the alarm which sounds like a doorbell goes off right where we are. And the alarm is portable if you use batteries instead of plugging in. We test it about every six weeks just to be sure the batteries have not died. The motion detector can be mounted at floor level near door frame or above the door frame. It is a great system and as a back-up, we have a front door alarm mounted on the frame in case the door opens. It’s loud and annoying but would wake you up. Motion sensor and chime/alarm was under $70 I believe.

I believe that she needs more care than her home can offer because you're not trained medical professionals. She needs care at one of the many different options out there. Good luck. God bless you.

My mother is in a senior residence memory care unit. The doors are locked and she wears a tracker anklet that sets off an alarm when she approaches any of the doors.

Oh my gosh, unless she can be watched 24/7 she needs more than home care. This is a safety issue. It’s too stressful to be a caregiver in this situation without having help. Please enlist help if she remains at home. Have you spoken to her physician to see what he/she recommends? Best of luck to you. Hugs!

@ Upstream: Oops. Forgot to mention that I'm 24/7 caregiver. She lives with my family and I take her home occasionally for visits. If there's a fire 🔥 I'll throw her over my shoulder like a sack of taters and run like... you get the he picture. 😁

Ditto. We changed the locks to key in and key out and kept keys with us. In case of fire this is not ideal but for keeping track of your mom... worked for us

Brought locks on Amazon. I’m at home 24/7 so we’re both locked in. I rather have locks than jumping up and trying to run after her, done that a few times after the police brought her home. I refuse to sleep one eye open every night, I need my sleep to be able to function. This stuff is already exhausting. So now she is safe and I’m safe and all is well.

HOLA CHICA,
Glad your loving dear mother is ok, thank the lord.
I would tie a bell around her (my mom does not have this dementia/alz.)but i would or something like a bell feasibly by the door, alarm, and or something by her side of the bed, for my dad to hear etc.al., but again mom is alright, she does not have that praise God.
and i pray for your mother.
My father has dementia, diagnose 2 and a 1/2 years ago. Doing alright most days and nights, thank GOD, and has not wander off ever, but gets up at night more than he used to, but he is hanging in there, doing better dr. say than most.
I pray for your mother(and her caretaker, you.)

adios.

Aznbobbo, if you have a store called Harbor Freight near you, they have door and window alarms for about 5 bucks for a 2 pack. Batteries included. I was in there today and saw them.

For the price and being battery operator I thought it would be worth a try. You might be able to order online.