A 17 year old could technically be in foster care until they are 18. The duty of the local authority now extends until 21 for young people who have been in care and then in further education.
After the age of 16, there is a tendency to turn foster care into supported living, but that doesn't mean they actually move out, I currently work with an 18 year old in that very same situation.
However it would be unlikely to be received into care at the age of 17, for the first time.
This is scotland I'm talking about, but I believe it is basicaly the same in England