I had booked myself DTW-STL and STL-LIT as two separate tickets ($34 and $39 internet fares), and booked my wife (Companion Pass) on one DTW-STL-LIT ticket (so there'd at least be a record of one connecting passenger in case of a delayed flight).

Due to bad weather in Chicago, our DTW-STL flight was, in fact, delayed and we missed our connection, to the last LIT flight of the night. The STL gate agent sent us to the ticket counter, where a supervisor apologized for our missed connection and said, "We don't normally do this because it was weather-related, but we're going to put you up at the airport Hilton tonight" and rebooked us on the first flight the next morning.

(The agent in DTW warned us of a misconnect and gave us the option of rebooking the whole trip for the next morning; we chose to try our luck with the connection, expecting only a "distressed passenger" hotel discount.)

Your experience may vary, but all of the Southwest employees we encountered that evening couldn't have been more apologetic and accommodating (even the Southwest pilots from another flight who shared the Hilton shuttle bus with us apologized).