What type of cane for Mom (96) with severe short term memory loss who lives alone?

She needs to be evaluated by a physical therapist and taught how to use a walker. Get her doctor to script a PT evaluation.

I wouldn't recommend a cane at this point. She would do much better using a rolling walker that has a seat. If she could manage one now that she is stooped over.

My late Mom [97] was also very thin and under 5' tall as she advanced in age. Mom would use her cane once in awhile, more so when we were out shopping. I noticed over the years Mom, who use to stand straight was now becoming very stooped over. And I believed it was from the cane, as she was stooped over to the side where she used the cane. One could see it when she wasn't using the cane.

Now my Dad had a cane for awhile but he preferred the safety of using a rolling walker. Dad is still standing straight being in his 90's. There were times when he would forget to use the walker thus it would be elsewhere in his house. Eventually his caregivers became Drill Sargents when it came for him to use that walker :)

FYI She has severe short term memory loss.

Get a walker , never a cane. She should NOT be living alone. Is this your mom? If yes, its time to take her home to live with you.

I agree, she should not be living alone. Though that is easier said than done.
Regarding cane, I would recommend a rolling walker. My mother with dementia uses a trifold roller walker inside our apartment and a rollator walker with seat when we go out.
She never got the hang of using a cane. Her balance was too unstable.
She loves the rollator; calls it her Cadillac.
I ordered both from Amazon.

My cousin's lack of short term memory caused her to constantly forget to use her her 3 legged cane. She would constantly walk outside over hilly ground without it, when she knew how poor her balance was. Multiple falls and fractures resulted. Eventually, we realized it was dementia. She was placed in Assisted Living and there she continued to forget to use it. Eventually, after a fractured spine, she ended up in a wheelchair.

I would find a way to have her supervised around the clock. She will likely fall and get fractures and it doesn't get better after that. Even that will not make them use a cane or walker.