Some people buy hotels, some people have a crashpad in base. The company won't cover you unless they have an already paid for room not being used (i.e. if a flight cancelled and the crew that was gonna occupy those rooms never made it). But don't count on this.

Air Wisconsin has the exact same rigs but only a three hour min day. We also have some instances where the company can classify a day as "No Min Day" if it ends early or starts late at the end or beginning of a pairing.

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Depends on base, but outstation bases are most definitely not commuter friendly. You may be able to get one end commutable after you get some seniority. DCA, EWR, LGA, and ORD are probably the most commutable bases. ORD is very senior for captains, but attainable as a FO. Don’t commute to outstation, because it will suck. Don’t plan on company ever buying you a hotel, but it can happen. I’ve seen it once in the last year.

You can call CS and ask if they have any extra hotel rooms. But like the other poster said, it is very rare that they have one available.