I’ve read some people ask their hotel in Rome if they can stay if test positive. I’ve asked 2 now and both have said no, Which hotels will keep you?
The moment they discover you are positive, the doctor responsible for your test will ask you if you have a place where to stay or not. If not, they will call the local branch of the SSN (national health service) who will find a room in a government-paid hotel in the outskirts.
A recent article on a local newspaper warned that a group of 6 Lithuanian tourists has been forced to wait 4 hours before a room was found in a so-called Covid-Hotel.
I know of someone who had an Airbnb allow it. You can check the website, see what is available for 10+ days, then message the owner to ask if it’s ok to stay there when positive.
Obviously only the entire apartment Airbnb’s, no one would want a single room in an occupied house for a covid case.