ways avoiding the need to sell property or home

If she gifts it to you or sells it to you for significantly under asking price, it is possible that creditors could reverse or undo the transaction as one designed to defraud them--keep assets from them--especially if she passes away shortly after doing this. (Medicaid, in particular, can do this, if Medicaid ended up paying for any of her care.) Therefore, if you and she are going to do this, do it NOW--you want as much time as possible to pass between the transaction and her passing; the more time that goes by, the harder it is for creditors to do this.
(Note: fair market value transactions can't be undone this way. So if she sells it to you for a fair value, even at the low end of fair value, you should be ok. Example: most property could reasonably sell for a range of value, depending on market conditions/timing and the buyer(s) you find. Say this home could reasonably go for between $250k - $300k. Since you'd avoid paying realtor's fees in a private transaction, she could probably sell it to you "as is" for between $200k and $225k, reflecting the lower cost of sale, so you'd get a good deal but the sale would be defensible.)
One option is for her to sell the property to you while retaining a "life estate" for herself. This will give her the right to live there for the rest of her life; and since you are not immediately getting the property free and clear (e.g. you have to let your mother live there for the balance of her life), that will justify you paying less than current market value for it.