my dad is 80 and has vascular dementia- he sleeps 16-18 hours a day and for not help with anything around the house. My mom is 81 and has degenerative disc disease and has had a couple femur fractures over the last two years- she is able to do laundry, some cooking- but struggles with strength- she is down to 110lbs and is emphatic about staying in their home.
Of course you will need to check references since you are not dealing with an agency.
1. Hire caregivers that can come help your parents.
I suggest an agency so that the caregivers are background checked. (although that is not a 100% guarantee that there will be no theft so keep ALL personal items under lock and key)
2. If you do hire but want to hire privately make sure you do background checks. That will generally show Convictions but may not show charges that have been dropped for any number of reasons. And hiring privately do it properly and have a contract and file proper papers for the IRS (if you are in the USA)
3. Begin looking for Assisted Living facilities. Normally I would not suggest AL for someone with dementia but with your mom there and with the help she would have from AL staff it might work. Or the other possibility is they could both reside in Memory Care.
I know mom wants to stay at home but if it is not safe for her to do so a move BEFORE an accident that will remove all options from her is a safer way to go.
You also might want to look into getting a Hospice referral for dad. A Nurse coming in 1 time a week to check on him (and I bet they would be checking mom on an "unofficial" basis) and a CNA that would come in and give dad a bath or shower and maybe help with changing the bedding.
The Nurse would order all medical supplies and medications and they would be delivered to the house. The CNA would order all personal supplies and those also would be delivered.
Part of Hospice as well a Volunteer can be requested and a Volunteer could come 1 time a week and either sit with dad while mom gets some time for herself, she can go out. Or the Volunteer request could be for some light housecleaning, grocery shopping or any number of tasks. (I am a Volunteer and I have walked dogs, weeded yards, along with sitting with a patient)