With exceptions, once you have paid for a ticket all commercial passenger airlines are obligated to transport you under their contract of carriage.
All airlines must do this, I even looked up the contract of carriage for the shittiest airline I could think of and Frontier has this to say:
>Involuntary -- If insufficient passengers volunteer, passengers who cannot be accommodated on the flight will be denied boarding and Frontier will provide transportation on a Frontier flight to the same destination. After a passenger’s boarding pass is collected or scanned and accepted by the gate agent, and the passenger has boarded, a passenger may be removed from a flight only for safety or security reasons or in accordance with Section 3 of this Contract of Carriage.
They must also compensate you. If being denied boarding delays you for 1-2 hours you get 2x the cost of the fare up to $1550 and 2+ hours 4x up to $2150.
And they still have to put you on a plane:
>A passenger denied boarding, voluntarily or involuntarily, pursuant to this section, will be transported on Frontier’s next available flight on which space is available and at no additional charge.
https://www.flyfrontier.com/legal/contract-of-carriage
Contracts of carriage are pretty much boilerplate but all of this is to say: if you pay, show up on time, and aren't denied boarding for a safety reason airlines are obligated to transport you to your destination.
(in the US)
