I currently know of 2 people who are not hired by a department and pwying their own way through the academy. I can find out what they did. They are technically self sponsors. The chief of a department has to agree to sponsor you, but you have to flip the bill for EVERYTHING. They have to buy ammo, gun belts, body armor,etc. You name it they have to eat the cost of it. The department "sponsoring" them may offer to help with some issues, but not required.
Check out the Lowell Police Academy. I graduated from there on 01/14/05 as a self sponsor. They are "certified" by the MPTC, but I think they are able to set their own rules when it comes to self-sponsors, so they may take you. I highly recommend it!