This seems to be answered reasonably well by the actual documents involved. The relevant US law requires that
(5)Entry into the United States
If arriving by sea or air, the alien arrives at the port of entry into the United States on a carrier, including any carrier conducting operations under part 135 of title 14, Code of Federal Regulations, or a noncommercial aircraft that is owned or operated by a domestic corporation conducting operations under part 91 of title 14, Code of Federal Regulations 1 which has entered into an agreement with the Secretary of Homeland Security pursuant to subsection (e). The Secretary of Homeland Security is authorized to require a carrier conducting operations under part 135 of title 14, Code of Federal Regulations, or a domestic corporation conducting operations under part 91 of that title, to give suitable and proper bond, in such reasonable amount and containing such conditions as the Secretary of Homeland Security may deem sufficient to ensure compliance with the indemnification requirements of this section, as a term of such an agreement.
and the actual form which constitutes the agreement requires:
- the Carrier meets the conditions to check ESTA status of VWP vistors before departure,
- the Carrier doesn't sell return tickets the visitor can then part refund or transfer (except in the country of issuance or nationality or residence of the alien),
- the Carrier agrees to meet the US governments cost of deporting anyone who isn't allowed in, and,
- the Carrier posts a bond to cover their costs/penalties from the previous year, as per the law above.