I was told by the chair of a department that admission to the program is separate from funding. He also told me that if I was offered admission at first, but not funding, that funding could still be possible. He gave me the contact information to the head of the graduate school and told me to contact them directly in that situation and inform them that I am interested in accepting the offer, but I can only do that if funding is made available. I was told that very frequently they are able to make funding available in these situations, in part because people who were offered funding will end up going somewhere else in addition to other funding sources they are able to consider.
Of course, this is one university. Your mileage may vary.
