> they will now just create a company in Singapore or Mongolia or another such place, which will then own the second home

How will that help to avoid a tax on secondary residences? Are they somehow going to claim that these properties are the primary residence of a company? Seems nonsensical.

No. The residence becomes an 'asset', and the original owner (and now owner of your friendly Mongolian NYC-condo-operations company [MNYCCOC]) now pays rent to the very same MNYCCOC as the landlord. They could even consider the condo to be a very exclusive one-suite hotel and pay by day, and deduct hotel costs for living in said condo as 'necessary business expenses'. In the meantime, the MNYCCOC is a good citizen, and pays taxes but only after ... and deducts everything necessary for upkeep, from dripping faucets to elevator repair to housemaids ('janitorial staff'), making them essentially free.

It's accountancy that makes the world go round round round...