We visited an old poured concrete basement that had one wall that was literally falling apart -- the others were fine. We tracked down roof and yard run-off that just feeds water to this wall all the time. This kept the wall completely saturated and although there were no obvious leaks, the fact that it was continuously soaked caused water to migrate towards the warm inside, where the water would then evaporate. But this moisture movement picks up salt from the concrete and that gets left on or just behind the surface. The salt crystals in turn expand and pop off the surface of the concrete. The process is called "spalling" and the white salt-like stuff is called "efflorescence".
This house has a dry basement, the water on the outside needs to be controlled. The roof needs rain gutters and the yard needs to be re-landscaped to get water away from this wall. Once that is done, all the loose stuff can be brushed off, the wall coated with a new coating of parging, and then they can insulate this wall without worrying about hiding problems or even creating new ones.