There aren't any teen shelters. Vin's predicament is rare. There's also the fact that he's so short - they think he's much younger than he is. They DO have their own Social Service type programs. Vin is registered with it so he can go in and get food, but he can't live apart from his mother and once they do register that she is deceased, they will look for a home for him with another family, but not until then. There are actually very few cubs 'lost in the system'. Most are taken in quickly by a family.
The social service program insures that families have enough to eat, decent clothes to wear, and takes care of the school supplies needed by students.
Adoption process is first come first serve Wolf society is geared toward the family and local society taking care of those in need below a certain age. The Akaelaes take it as a personal pride to be able to help many, but, the 'adoptions' in name are on varying degrees. They are wards of the Akaelaes who see to it that they are educated well and treated well to expand the influence of their family name. There are not any orphanages in Wolf society, displaced cubs are usually quickly dispersed among the local society. There are varying levels of this throughout Cyantia, with some putting orphans into the same category as servants/slaves up to a certain age. You'll see some of this in Genoworks Saga.
They tend to care well for their cubs because they have to depend on their cubs to take care of them when they are elders. (And the more cubs they have, the more that care can be dispersed amongst them Most females just don't really want to have a whole bunch of cubs themselves.