Good Questions.
The asset is legally tied to the token by the tokenization process.
Token holder rights are defined by the smart contract and described in the security token offering where the tokens are sold. Since these are registered securities, the token holders are protected by securities laws in each country.
An example would be that the security token offering defines the rights of token holders in terms of price appreciation and earnings from the property in terms of rental income. If you own 1 of 1000 tokens you are entilled to 1/1000th of all price appreciation, in addition to return of your capitol investment, plus 1/1000 of any income derived from the asset/property such as rents.
The lower cost also allows diversification of investments lowering your risk.
If you are the home owner you simply need to retain 51% of the tokens to maintain control of the property, and make sure the security token offering states you retain control, and then to entice buyers you will need to provide income so there is a ROI on the investment without selling.