So far as I know there is no flexible soldering technology, and creating one would be pretty extreme materials science.
There are already polymer glue solder alternatives. They are nowhere near as good as solder, however.
The normal solution is to make the PCB stiffer... Fundamentally a long flat thin object is going to be bendy or brittle
What about changing the layout, such that you can introduce many, many voids in the circuit board? If you can divide up the board into many separate "compartments" then each individual segment can be proportionally stiffer and less flexy. (Long, thin things are "bendy" because the material can act as a lever against itself, so many short stubby things can be very stiff locally.)
There are already polymer glue solder alternatives. They are nowhere near as good as solder, however.
The normal solution is to make the PCB stiffer... Fundamentally a long flat thin object is going to be bendy or brittle
What about changing the layout, such that you can introduce many, many voids in the circuit board? If you can divide up the board into many separate "compartments" then each individual segment can be proportionally stiffer and less flexy. (Long, thin things are "bendy" because the material can act as a lever against itself, so many short stubby things can be very stiff locally.)