The lands registry will not allow sub-units to be sold and registered in a new name, but rental is common, and probably not illegal (lawyers may weigh in on this). When Tel Aviv attacks the problem, they prosecute the building owner not for the rental itself, but for the physical changes made in the building. The Design and Building Law prohibits all changes to buildings once they are licensed and built. However the physical difference between a whole apartment and a subdivided one are elusive and subtle. Do we prohibit lock-able doors within apartments? Most apartments have 3 or more of these already! Are we counting kitchens and bathrooms? The most common legitimate apartment renovation adds a second bathroom and often a kitchenette.
In any case prosecution under the Design and Building law is complicated and protracted. Judges often rule in favor of the municipality, only to give an 18-month grace period to fix the violation or license the change. Architects in Israel, embarrasingly enough, are proud experts in the evasive tactics available to them to get around their own law. I have often been asked to design apartments and houses that are "ready" for subdivision, or include tricks to steal extra area or limit prosecution. Contractors routinely refer to "Phase One", the construction as per the building permit needed to get a Certificate of Occupancy, and "Phase Two", the planned violations carried out after the Certificate is in hand.
In any case, it is not the physical arrangement of the subdivided flats that is the problem; it is their use, and the business arrangements surrounding their use. I propose dealing directly with these arrangements using the authority most suited to gather information on business dealings: the tax authorities.
The income tax authority can act quickly to reclassify a particular deal and remove exemptions. In the case of privately owned rental apartments, the tax exemption is substantial. Are owners of subdivided apartments really entitled to this generosity on the part of the state?
Overcrowding the residential environment lowers health standards, increases the risk of catastrophic fires, and burdens the infrastructures of streets, sewers, and utilities. The land use in these areas has been transformed from residential to more of a hotel or hostel use. Luckily, the legal structures already exist to regulate, tax, and control these sorts of businesses for the public good.
I recommend reclassification of these properties within the regulatory structure of hotels and hostels. Rezoning of the neighborhoods could lag by years or even decades, but the immediate benefits are apparent. First and most importantly, the existing laws regulating hotels would insure standards of health and fire safety before lives are lost. Taxing owners as regular business operators would be a truer representation of their activity and provide tax revenue that is now lost. A third benefit would accrue when the newly regulated and taxed hostel industry drives out the worst of the profiteers.