The IRS could do an audit and determine it was designed to avoid tax. They would be concerned that the conditions put on the gift don't make it a gift. As JoeTaxpayer noted in the comments - This is known as the "Step Doctrine" which refers to a series of individual events or transactions, each of which is fine, but when looked at in their entirety, form a full transaction that's not permitted.
The transfer could trigger the local government to reappraise the house, in some cases that could lead to a large increase in property tax.
Some jurisdictions give tax breaks to senior citizens who have a low net worth, this gift could end that.
The receipt of the gift could complicate Medicare if the parent needs to enter a nursing home.
They could put whatever they want in their will, and give it to anybody.
Advice from my Phd tax professor:
Have the dying parent gift it to a child or someone else. The stepped basis would look at the gifts being transferred back and forth and determine that it was not a gift in the first place as mentioned by mhoran_psprep.
The alternative is to have it adsorbed in the person's unified credit against estate tax. § 2010
Lastly, make sure you check U.S. Code § 2515 for generation skipping and the taxes assumed by people making gifts to others in family when the gift is property/ estates.
As you have described your situation (single parent, etc.), it is a viable and commonly used strategy. There is a potential pitfall not mentioned that absolutely applies to your scenario. The gift must be made to the parent at least one year prior to the parent's death to avoid triggering Section 1014(e) of the Internal Revenue Code.
Sec 1014(e) states that if a gift acquired by a decedent within 1 year of DOD passes back via the estate to the original donor of the gifted property, there is no step-up in basis. The basis of the property upon receipt by the original donor will be the adjusted basis the property in the hands of the decedent as of the DOD.
This is a commonly used strategy in California. The two biggest potential pitfalls already have been discussed: gift recipient doesn't survive for a full year and possible violation of the step doctrine.