I just e-mailed the migration office to get something in written form but they just referred me to this document, which is in German: https://ma.zh.ch/internet/sicherheitsdirektion/migrationsamt/de/rechtliche_grundlagen/bewilligungen_einreiseundaufenthalt/_jcr_content/contentPar/downloadlist_0/downloaditems/erwerbslose_wohnsitz.spooler.download.1503040097825.pdf/Erwerbslose+Wohnsitznahme+aus+Drittstaaten_IW.pdf

Last time I called Zurich’s migration office (+41 43 259 88 00), the lady was pretty nice and assured me that with enough capital they would consider giving out a private visa and recheck after a year if the person can still sustain on his/her own. It would be interesting to find out if one can work/get employed while on that visa. Should I call them for you to find out?