There are some variations in the 'how' question .. but in short , some are not crystalline ... these can be very durable ... some will not crack ... they can still be damaged and stop working ... but some of them can take allot of flexing and allot of punishment.
Don't forget the roll the adhesive will play as well ... the adhesive will also have to allow for flexing ... if the adhesive cures ridged, it will impair the ability of the flexible cells to flex.
Now for the bad ...
The flexible cells are significantly more expensive $ per watt of power.
The flexible cells are significantly less efficient and will produce less electrical energy under the same conditions and coverage.
Many of the flexible cells degrade much faster over time than the crystalline variations do... so 20 or so years from now don't expect the same kind of 80% initial power output many of the crystalline style cells offer.
So there will be a trade off.
Are there specific flexible cells you are looking at?