I think more generally, protein folding happens at the RER and the stem says the protein doesn’t fold properly. Specifically, the most common CF mutation is a misfolded protein and the protein is retained in the RER and not transported to the cell membrane - FA 2019 pg 60.

The CFTR protein is a transmembrane protein. Like all proteins, its translation begins in the cytosol; that said, CFTR contains an N-terminus “signal sequence”, which means as it is being translated, it (and the ribosome making it!) will be transported to the Endoplasmic Reticulum.^footnote!

As it gets translated, its hydrophobic motifs will emerge, which embeds the CFTR protein within the phospholipid bilayer of the ER itself! That means the protein will never again be found “in the cytosol” because it gets threaded through the bilayer (which is, in fact, how all transmembrane proteins become transmembrane proteins at the cell surface -- they have to be made into transmembrane proteins in the ER first!).

So, yes, ultimately, these misfolded proteins will be directed toward a proteasome for degradation/recycling, but that will happen as a little vesicle (or “liposome”); the misfolded protein, in this case, is not water-soluble (since, by definition, it has hydrophobic motifs which get “threaded through” a bilayer to create the transmembrane pattern), which means you won’t find it in the cytosol.

\ footnote! \ The hitching of active* ribosomes to the Endoplasmic Reticulum is why we call that area of ER “rough Endoplasmic Reticulum (rER)”; on electron microscopy, that section was bespeckled with little dots; later, we (humans) discovered that these dots were ribosomes!

\ * \ By “active ribosomes”, I just mean ribosomes in the process of converting mRNA to protein! (What we call “translation” ;)

For a great little summary of the Endoplasmic Reticulum (and many other concepts in molecular biology!), see this from Alberts’ Molecular Biology of the Cell:
https://www.ncbi.nlm.nih.gov/books/NBK26841/#A2204

When proteins being made in the ER misfold, they accumulate in the ER, which then triggers them to be spit out into the cytosol and become degraded by proteasomes. Thus, the accumulation of the misfolded protein in the ER is required for them to ultimately be tagged by ubiquitin and be degraded in proteasomes.

Even if you argue that they will be accumulating in the cytosol because proteasomes are in the cytosol, the question is asking where are the proteins accumulating, not being degraded. So they can't accumulate in proteasomes, because they are destroyed in them.

This is from amboss: Mutated CFTR gene (ΔF508 mutation) → misfolded protein → defective protein is retained in the rough endoplasmic reticulum (rER) for degradation → ATP-gated chloride channel is absent on the cell surface of epithelial cells throughout the body (e.g., intestinal and respiratory epithelia, sweat glands, exocrine pancreas, exocrine glands of reproductive organs)

ULTRA SIMPLE.

1.there are many variants of cystic fibrosis so this question is not about pathyphys. of CF

2.point of question : where does protein folding occur ? answer) RER

1. IN THIS TYPE OF CF , if protein isnot folded properly in RER will it go out or will it accumulate ? answer) it will accumulate in RER.

TIP : IF YOU KEEP RESEARCHING ON VARIANTS OF CF, YOU ARE ON A PATH TO ENDLESS DOOM