How could the Shuttle remain....

[Urwumpe]

What would happen to the crew of a space shuttle if they couldn't get the bay doors to close? Would they just have stay up there until NASA could get them down?

If all other ways fail - yes.

Reentry is not possible with open payload bay. It disturbs the aerodynamics otherwise, which would mean that hot plasma touches surfaces, which are not protected against them - for example the aft compartment.

 

[Lunar Pilot]

Anyway . . .

Besides, I don't even like the Space Shuttle anyway. Because originally it was designed to be a cheap, fast way to freight things like satellites and space station modules into LEO. However, considering that they spend 2 billion dollars refurbishing the shuttles after every mission. Per shuttle. I would guess that that isn't the cost-efficient design NASA was hoping for in the 1960's.