Property management companies Ie Bridgestreet

It is called Weworks.

To clarify this is for individual residential units.

I am not aware of any firms that do this- though it doesn't mean that it doesn't exist. That said, you are aware that it's pretty common in Manhattan to have the tenants pay the broker fee (especially during the summer), right? That is something that isn't common in other rental markets. If your apartment is priced right, it shouldn't remain vacant.

All coops and many condo buildings will forbid subletting.

Doesn't Bridgestreet manage corporate apartments, extended-stay apartments and other short-term rentals advertised on Airbnb and other websites? I don't know their business model but I suspect their fees are quite high.