They are (out) in Brazil, and they fear being stuck there: unable to leave.
"Stuck out" is not used as an expression here, but as two separate words. [It's an easy mistake to make.]
In informal British English we sometimes use out when speaking of foreign countries:
I have a brother out in India.
I might go out there myself next year.
[Perhaps it's rather old-fashioned. I can't find this usage of 'out' in a dictionary.]
To be/get stuck means to be/get fixed in a particular position or place and unable to move or be moved.
Sara tried to open the window but it was stuck.
We got stuck in a traffic jam.
If they are/get stuck in Brazil it means they can't leave the country. They can't get home. (Perhaps there are no planes.)
If they get stuck out there, they will just have to stick it out! (That DOES mean 'endure it'!)
Lexico (See definitions 4.1 to 4.4 of the verb 'stick'.)