If they are overbooked and need to bump passengers, they will ask for volunteers first. It has no bearing on who paid what price for their tickets. Even if you were the last person to buy a ticket for that flight, doesn't mean you'll be asked to rebook. Often, when a flight may be overbooked there are already people that have asked to be placed on the a bump list, so they'll go to those volunteers first and you'll never "hear" about it. The airline will put the volunteer on a guaranteed seat on the next available flight, plus give them a reward of some kind, usually a voucher for a free round trip up to a certain dollar value. They will keep upping the ante until they get the number of volunteers that they need. If you decide to volunteer, you will not have to pay a dollar to rebook.
Now, that said, can they force you? I suppose...anything is possible, however not likely as they will go the volunteer route first and most likely will resolve the overbooking this way.
We came back from Disney once and our flight was overbooked. My DH and DD decided to take the bump and return on the first flight the next day. The airline put them up in the hotel in the airport, two round trip vouchers, and gave them meal vouchers for dinner. They loved it...it was an adventure to them.