Any artificial concurrent computing system involves a potential risk of "deadlock" that its multiple processes sharing common computational resources are stuck in starved conditions, if simultaneous accesses of the processes to the resources were unconditionally permitted. To avoid the deadlock, it is necessary to set up some form of central control protocol capable of appropriately regulating the resource allocation. On the other hand, many decentralized biological systems also perform concurrent computing based on interactions of components sharing limited amounts of available resources. Despite the absence of a central control unit, they appear to be free from the deadlock implying their death, as long as they are alive. Should we consider that biological computing paradigms are essentially different from artificial ones? Here we employ a photosensitive amoeboid cell known as a model organism for studying cellular information processing and construct an experimental system to explore how the amoeba copes with deadlock-like situations induced by optical feedback control. The feedback control is implemented by a recurrent neural network algorithm for leading the amoeba to solve a particular constraint satisfaction problem. We show that the amoeba is capable of breaking through the deadlock-like situations because its oscillating cellular membrane spontaneously produces a wide variety of spatiotemporal patterns. The result implies that our system can be developed to a neurocomputer that works as logical circuit, associative memory device, combinatorial optimization problem solver, and chaotic computer capable of spontaneous transition among multiple solutions.