If some of the axons innervating a given cell are destroyed or if they become inactive, what compensatory process takes place in the remaining presynaptic cells?

The question is incomplete as it does not have the option which are:

activation of previously silent synapses removal of toxins denervation supersensitivity collateral sprouting

Answer:

Collateral sprouting

Explanation:

Collateral sprouting refers to a process in which the neurons which are still alive after they are destroyed or inactive, grows or sprouts its axons to the disabled territory.

The collateral sprouting is observed in the case of the somatic nervous system when the muscles are injured or destroyed. The motor neurons present in the injured part sprouts its axons to the muscle to keep them reinnervate and functional at that time.

In the given question, since some of the innervated axons get destroyed therefore the other axons will undergo collateral sprouting.

Thus, collateral sprouting is the correct answer.