Still a sandbox -- nothing in a sandbox precludes a world that evolves, particularly evolution caused by player choice.
Hopefully if a GM runs a published adventure or self-written one, the world also evolves and adjusts as players make unexpected choices.
You're starting to run the adventure to save PC#1's grandma. The PCs have opted however to stay home and go take out the mob boss who's been bothering their favorite innkeeper. You only made up the mob boss as some flavor last week.
what do you do:
a) force them to rescue grandma by guilt, by "your not in character, by force or override)
b) make up some stuff so the mob boss is behind the grandma problem so you can re-use the material
c) make up a whole crime syndicate and run that. Meanwhile, Grandma dies
d) Make up some material for the mob boss and his goons for the PCs to hunt down, meanwhile word of Grandma's escalating problem arrives
Choice A is always bad.
Choice B is still the grandma adventure, but you trying to bring it in on the angle the players want to pursue. Depending on how this is done, its OK, but it might also be done badly.
Choice C is the DM being flexible and punishing at the same time. Sure, you just finished doing this cool thing, by the way you chose wrong.
Choice D is similar to C, except that the GM softens the outcome of the choice, thereby letting the players take another stab at the decision. In theory, the grandma adventure should have gotten harder (which is OK, because the party just leveled up).
I'm not a big fan of choosing the most extreme outcome for a player choice. The DM can stagger the ramp-up of consequences, giving the player a chance to reconsider and re-evaluate. I'm also not a big fan of letting an ignored problem remain as it was while the party does something else.
So I don't give them too many simultaneous problems. And I consider what's a middle ground consequence that I can reveal while the party goes and does something else. To me its more natural in that if you don't pay your rent, you don't get evicted the next day, you get notices and warnings.