Aging and neurodegenerative diseases, such as Alzheimer's (AD) or Amyotrophic Lateral Sclerosis (ALS), led to widespread degeneration of long-range connections in cortical structural connectivity (SC). These damages manifest as losses in connections or demyelination of axons. When the SC of the brain is damaged, the functional connectivity (FC, i.e. the dynamic interactions and information exchange between distinct brain regions) is locally and globally perturbed. Despite the close correlation between SC and FC, they are not identical; FC exhibits greater flexibility and can reorganize in response to SC damage, suggesting the existence of compensatory mechanisms that maintain FC homeostasis. Using a combination of theoretical models and computational simulations, we demonstrate that it is possible to modulate local dynamics within brain regions to preserve FC despite severe SC damage. Specifically, we propose that widespread modulation of local excitatory and inhibitory conductances may allow the system to remain in the same dynamical regime of operation so that the same pattern of interareal interaction can be enabled. This finding suggests a dynamical rather than structural basis for maintaining functional brain organisation, offering new insights into the brain's resilience to neurodegeneration. We suggest that the brain's ability to maintain cognitive performance levels despite SC degeneration may be underpinned by dynamic compensatory mechanisms. This opens up potential avenues for therapeutic interventions aimed at modulating local dynamics to restore global FC, thereby offering hope for treatments targeting the dynamical state of the brain rather than attempting to repair structural damage directly.