  Entangled systems in experiments may be lost or offline in distributed
quantum information processing. This inspires a general problem to characterize
quantum operations which result in breaking of entanglement or not. Our goal in
this work is to solve this problem both in single entanglement and network
scenarios. We firstly propose a local model for characterizing all entangled
states that are breaking for losing particles. This implies a simple criterion
for witnessing single entanglement such as generalized GHZ states and Dicke
states. It further provides an efficient witness for entangled quantum networks
depending on its connectivity such as $k$-independent quantum networks,
completely connected quantum networks, and $k$-connected quantum networks.
These networks are universal resources for measurement-based quantum
computations. The strong nonlocality can be finally verified by using nonlinear
inequalities. These results show distinctive features of both single entangled
systems and entangled quantum networks.
