In the US, the CDC will bill an individual's health insurance provider, but the government absorbs the cost otherwise (possibly passing the costs on to Medicaid). It is not clear whether the military bases where quarantinees are sent will charge the CDC room and board (to be passed on to insurance companies, Medicaid or other outlets).
Since the last quarantine order in the US was 50 years ago, for smallpox we are in kind of uncharted territory. In the hypothetical scenario where housekeeping staff in a luxury hotel are stuck there for a 2 week quarantine, the employer (hotel) bears the cost for complying with a government order that nobody can leave the hotel.
The quarantine order states that
Components of the Department of Health and Human Services (HHS),
together with state and local public health partners, will arrange for
adequate food and water, a continued place to stay on [place of
quarantine], medical treatment, and a way for you to communicate with
a family member or another representative while you are held in
which in lieu of a statement that you must reimburse the government is reasonably to be interpreted as a promise to arrange and cover costs, not just arrange. 42 USC 249 states that
(a) Any person when detained in accordance with quarantine laws, or,
at the request of the Immigration and Naturalization Service, any
person detained by that Service, may be treated and cared for by the
Public Health Service...
(c) Persons whose care and treatment is authorized by subsection (a)
may, in accordance with regulations, receive such care and treatment
at the expense of the Service from public or private medical or
hospital facilities other than those of the Service, when authorized
by the officer in charge of the station at which the application is
The question of whether an individual will be required to reimburse the government for risky behavior depends on the nature of the existing government order. I don't believe that the CDC has the authority to prohibit travel to some place (such as Wuhan), though if it is in the US they can prohibit entry into said place. Of course, the law can change with circumstances.