Decades ago I saw where a company had purchased a large number of buildings that were all condos. They were offering "virtual" time shares where you could buy in and apply your share to a few weeks or months in any one of their properties, provided there was a vacancy. Has anyone seen anything like that?
Could be but there is nothing stopping someone doing it legitimately. Just like a time share on a plane but instead of a single plane its on a fleet. A hotel chain could do it. You buy a "room" of a particular class and small monthly fee similar to a condo and you can go to any hotel in the chain and stay as long as you like. I think it would make more sense though for larger more luxurious apartments.