The reason eldercare decisions are so tough is that you don't have any idea how this whole next few days, weeks, months, years will play out. If your mother has enough money to put her in a "memory care" type assisted living and self pay, let that be your next step. As long as she is self paying, there will be no need to take any actions on her house. And then it becomes a day to day situation. With no way you can predict or pre plan at this point.
She might have a sudden heart attack or fall or stroke and pass away after being there ten days. We hope this isn't the case, but it could happen. Say she lives several years happily in this unit, (which we hope for you of course) and runs out of money other than her pensions. The next step would be either to sell her house and use the assets from the sale to continue to fund her stay there, or to try to get placement for her in a nursing home and certify her for Medicaid, which would, at that time, require a complete assessment of her assets (the home) and a lien against it. Most nursing homes are very helpful in these issues, as they definitely wish to be paid.
But to put it bluntly, you have no idea how long she will live or what condition she will get in before she passes away. If you could, and did purchase the house from her now, and she files for Medicaid soon, any proceeds from the sale of the house would be in her accounts and would be taken to pay for her care before she was eligible for Medicaid. If she deeded the house over to you and applied for Medicaid before five years from the date of the transfer of the house, it would be regarded as an asset and she would be penalized in her eligibility for Medicaid. They have a five year "look back" when doing certifications for eligibility.
You make it sound like you think the state and federal government should not be paid for her health care if they are asked to provide it , that they might "seize" your mother's property unjustly. That's just not so. It would be honest and proper to use her assets to pay her medical bills, IF if becomes necessary.
But if she is actually admitted to a nursing home after a health care crisis, a few days in the hospital, Medicare will pay for a while, usually about 90 days. To be blunt, most elderly people do not require long long stays in a skilled nursing facility under these circumstances, they do not last that long once their health declines sharply. If I were you, I'd not at this point try to do any big pre-planning. Just move forward to the next step and see how things play out.