Detection of nuclear recoils produced by coherent scattering of low energy solar or reactor neutrinos appear to be possible with the next generation of detectors, and several large projects are setting this goal. Yet we foresee unexpected difficulty on this path: self-organized criticality (SOC) in the system of long-living excitons can result in a detector-generated low-energy background resembling the response to low-energy nuclear recoils. SOC conditions are not unusual in condensed matter physics and can be identified and treated. Here we discuss how SOC effects in the dual-phase detectors can be experimentally verified and the unwanted background suppressed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Presentation given at the Magnificent CEvNS workshop (2018).