Taking into account that c-Fos activity reflects the last part of this process of extinction in this study, we cannot preclude the possibility of a new inhibitory learning taking place at the time. According to some authors, the extinguished memory is not erased but inhibited, so that the observed c-Fos changes may reflect this new learning process that could be occurring at the end of the extinction procedure.
Researchers seem reluctant to say that c-fos is a causative part of making the neuronal assemblies associated with addiction, but they do find a strong correlational link:
The described neurochemical and molecular biological mechanisms all support the idea that c-fos promoter activation is an indicator of strong and persistent calcium influx into synapses of MSNs that received the most excitatory glutamatergic input. Drug-induced dopamine can synergistically enhance c-fos promoter activation in these strongly activated MSNs. It should be noted that a lack of Fos expression in a neuron does not imply a complete lack of neural activity, only that it is not depolarized strongly or persistently enough to produce enough intracellular calcium to activate the ERK signaling pathway. The earlier section describing in vivo electrophysiology and cellular imaging studies indicate that the neurons receiving the most excitatory glutamatergic input are determined by the context and cues present during drug administration. Altogether these data support the hypothesis that Fos-expressing neurons in corticostriatal circuitry can act together as a unit to form neuronal ensembles that encode and mediate conditioned drug behaviors. It is important to note that we treat c-fos and Fos only as markers of activated neurons in this hypothesis and do not imply that these molecules are directly involved in neuronal ensemble function.
Suppose someone wants to learn a new behavior or lessen the pull of a learned, unhelpful behavior. Might it be helpful to increase c-fos somehow during the learning/unlearning period? Delta-fosB, which I discussed in previous posts, accumulates in addiction and represses c-fos, which repression could be preventing addiction-breaking learning/unlearning. That gives support to the idea that not increasing c-fos is unhelpful when overcoming an addiction. But it does not logically follow that increasing c-fos will therefore be helpful in overcoming an addiction. I'll have to look and see if there are studies done specifically on that.
There are studies that look at how to increase c-fos expression. Three tested ways to increase c-fos expression are forskolin (an herbal supplement already in use by some as a weight loss help), BDNF (brain-derived neurotrophic factor, a protein), and membrane depolarization (brought about via neurotransmitters or KCl) (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4696896/). BDNF is being looked at as a possible aid in cocaine addiction (https://www.ncbi.nlm.nih.gov/pubmed/26923993), and forskolin seems able to induce a strengthening of synapses involved in memory formation (but the effect is much smaller in older rat brain tissue--https://www.ncbi.nlm.nih.gov/pubmed/15911893). Glutamate is a neurotransmitter, and monosodium glutamate (MSG) is known to evoke c-fos activity (https://www.ncbi.nlm.nih.gov/pubmed/26762887); a quick Google search finds that many people feel MSG is addictive for them, for what that's worth.
Here's a fun idea to test whether upping c-fos helps develop new brain pathways associated with memory and addiction. Try a new activity that you would like to become slightly addicted to, and eat Nacho Cheese Doritos while you do it. Nacho Cheese Doritos are a good source of MSG. Then see if you are more fixated on the new activity afterward than you would have expected. Even if the experiment bombs, you'll have gotten to eat Doritos in the name of science!