Southwest's conditions of carriage say (page 29, which is page 30 of the PDF):

7. Baggage

[...]

i. Limitations of liability

(1) General. The liability, if any, of Carrier for loss of, damage to, or delay in the delivery of Checked or carryon Baggage and/or its contents, with the exception of wheelchairs, mobility aids, and assistive devices used by a Qualified Individual with a Disability, is limited to the proven amount of damage or loss, but in no event shall be greater than $3,500.00 per fare paying Passenger [...]

(3) Baggage Delivery
(i) General. Carrier will pay delayed Checked Baggage delivery charges only so long as such Baggage was tendered to Carrier by the Passenger at least 45 minutes prior to the scheduled departure time of the Passenger’s first flight. If a Passenger’s Baggage is tendered to Carrier less than 45 minutes prior to the scheduled departure of the Passenger’s first flight, Carrier will make reasonable efforts, but cannot guarantee, to transport such Baggage on the Passenger’s flights, and Carrier will not assume responsibility for delivery charges if such Baggage arrives at the Passenger’s destination on a subsequent flight. See Section 8 for conditions applicable to international travel.

Section 8 is about the Warsaw/Montreal convention and I'm fairly sure it's not relevant here because your travel with Southwest is not international.

My interpretation is that, as long as you check your bag in at least 45 minutes before departure, Southwest will pay up to $3500 to deliver your bag to wherever you are. Shipping a bag anywhere in the world costs much less than $3500, so that limit isn't going to affect you.