Hi jumping_gene,
I revisited the HDB web site. Foreigner is allowed to rent the whole HDB flat. However, I am not sure how many the HDB flat owner who is eligible to rent out their flat. You may have a look at it. Anyway, you can try your luck...
Eligibility of Flat Owners
Subletting of whole flat is allowed in sold flats. You are allowed to sublet your flat if you fall under one of the following circumstances :
You are living in quarters provided by employer
* You/your spouse, your family members or authorised occupiers, are all staying in quarters provided by your employers.
You are going overseas to work or study
* You/your spouse are going overseas to work or study and the entire family will be going along, or you are leaving behind family members who cannot take care of themselves and who will be moving out of the flat.
You are living in commercial properties
* You/your spouse are tenants, subtenants or owners of commercial
property with living quarters and you have to stay there, with your family members, to look after the business.
You have satisfied a 5-year or 10-year Minimum Occupation Period (MOP)
* You have occupied your flat for at least 5 years and do not have an outstanding HDB loan; or
* You have occupied your flat for at least 10 years, regardless of your mortgage loan status i.e. you may have an outstanding HDB loan.
Other circumstances
* You are the sole owners and occupiers of the flats and need care from relatives because of illness.
* You are the sole owners and occupiers of the flat and are hospitalised for more than six months.
* The flat owners have passed away and left behind an orphaned minor child (i.e. child under 21 years of age). The guardian or public trustee of the minor child may sublet the whole flat.
By the way, any expats is renting the whole HDB flat? May be you can share the information with jumping_gene.