Michael Bidwill mentioned the other day -- after Bruce Arians and Carson Palmer had announced their retirements -- that the Cardinals didn't have a coach or a quarterback in 2013 for a time, and that worked out OK. So being without both right now is not a concern. The coach situation will be sorted out sooner rather than later, and then comes the QB. What exactly will happen is TBD, in part based on whoever the coach will be. Besides, a shift in QBs (with Palmer's retirement) is often coming with a new coach.
The Cards were looking for a new QB in 2013 as Bidwill noted, but unlike now when the non-Palmer QBs all have expiring contracts -- Drew Stanton, Blaine Gabbert and Matt Barkley -- the Cards actually did have quarterbacks they could have kept in 2013 when Arians arrived. They actually had four as free agency began.
Kevin Kolb, beat up as he was, was due a big contract. John Skelton was still around, as was Ryan Lindley, and the Cardinals even extended a tender offer to restricted free agent Brian Hoyer for 2013. When Stanton signed as a free agent the second day that was possible, the Cards basically had four QBs. A couple of days later, the team let Kolb go. When Hoyer finally signed his tender offer on April 1, the team released Skelton. Palmer arrived the next day in trade. Hoyer was later released in mid-May. Lindley stuck around as the third QB that season.
There is much more up in the air right now. There is no pat hand to play, unless one or more of the FAs-to-be get an extension -- which could happen. There were at least placeholders back in 2013, had the Cards not found what they wanted.