How does an airliner deal with cabin altitude at an airport above 8000 ft?
Here is the text extracted from Boeing's 777 Flight Crew Operations Manual:

In cabin altitude controller cruise mode, maximum cabin altitude is 8,000 feet. When the takeoff field elevation is higher than 8,000 feet, the cabin descends to the cabin cruise altitude while the airplane is climbing.
When the destination airport elevation is greater than 8,000 feet, cabin altitude controller cruise mode maintains a cabin altitude of 8,000 feet.
(...)
At touchdown, the outflow valves open to depressurize the cabin.

Therefore, when the airplane is on the ground, its cabin altitude is always equal to the ambient altitude. When it is in the air, the maximum is 8000 feet. Whether the cabin altitude will climb to 8000 feet or descend to 8000 feet depends on field elevation.
The reverse happens upon landing. If landing at an airport at 10,400 feet, the cabin altitude is &lt;= 8000 feet until touchdown, then raises to 10,400 feet.
This make sense - if the outside pressure is greater, how do you open the door? (well with enough force you can, but I will leave it to your imagination as to what happens the moment the door is opened).