Eventually- and I have no idea how long that is - it will be possible to fold/unfold a screen. It is already technically possible to roll and unroll a large tv screen, and at least one company says theirs will soon be available.-
LG ROLL Up SCREEN. So it's not impossible just technically difficult right now.
The cost is going to be high for a foldable phone, and it probably produces a very big phone or an average to small Pad computer, depending on if it is folded (phone) or unfolded (iPad). Even if the screen is durable, I don't know that they will sell a lot. They are very expensive, and likely to remain so, and every 2 or 3 years processor or graphic power improvements make the fold-a-phone less powerful compared to even middle of the road newer non folding products. There may be a market for a $2000.00 plus phone, but that market is smaller than the current $1100 to $1400 phones that the top phone makers sell now. And they haven't done that well. Now imagine trying to sell an upgraded version every year. Phones in general have gotten too expensive for a lot of people, and this will shrink the premium phone market even more.
Unless some breakthrough brings costs way down.