What happens if the crew do not set a FLT ALT in the cabin pressurization panel and leave it at zero but AUTO is still selected?
Consider a similar scenario: the crew selected 28,000 feet, cruised at 28,000 feet, but then step-climbed to 34,000 feet without selecting the higher altitude for pressurization.
The crew operating manual makes no mention of either scenario, unless you read between the lines. The way I tackled those scenarios is by referring to the controller logic in the manufacturer's patent from 1981 (the same digital controller was optional on the 737 Classic):

When the cruise altitude controller senses that the aircraft altitude change is within selected limits [when approx. 1,000 feet below FLT ALT], the system clamps to a scheduled value of cabin altitude [see second note below] (...)
If the aircraft cruise altitude drifts sufficiently to exceed ±500 feet from the altitude at which cruise control was imposed, the cabin altitude simply unclamps and the cabin climbs or descends at a predetermined rate under the control of central processing unit 54. (...)
Central processing unit 54 computes the differences between the pressure altitude and the value of Hcruise-clamp once per minute. If that difference exceeds the predetermined valve Hcruise-clamp is assigned the value of the pressure altitude.

Based on that, after leaving the ground mode (or lower cruising altitude), the controller will still pressurize the cabin – but not in reference to the DP schedule when cruise is reached (see second note below).
During descent (based on both the crew operating manual and patent), the controller will engage the off-schedule descent mode – landing altitude being the same as the departure airport altitude that was automatically sensed and set in ground mode – the crew will be alerted to that.

Notes:

In newer planes the pressurization controller is simply fed this data from the FMS (CDU or MCP entry).
Unlike other jetliners that maintain a cabin altitude with varying differential pressure (DP) for comfort, the 737 maintains a DP based on altitude blocks (consistent structural loads) when the FLT ALT is set. If you don't have the manual, b737.org.uk covers that part and offers a good system description.