If local government does work that is typically done by the central government, it is possible, but there are several factors to consider. Here is a detailed explanation of how this can happen:

1. Devolution of Power:
In some countries, there is a system of devolution, where certain powers and responsibilities are delegated to local governments by the central government. This allows local governments to take on tasks that are traditionally handled by the central government. Devolution can vary in degree, with some countries granting more autonomy to local governments than others.

2. Decentralization:
Decentralization is another way the local government can take on central government work. It involves redistributing power and decision-making authority from the central government to lower levels of government. This can include financial resources, administrative functions, and policy-making. By decentralizing power, the central government can transfer some of its responsibilities to local governments.

3. Regional Disparities:
In countries with significant regional disparities, local governments may step in to address the specific needs and challenges faced by their communities. They may take on additional responsibilities to bridge the gaps in infrastructure, healthcare, education, and other essential services. This is especially true in federal systems where local governments have more autonomy.

4. Efficiency and Proximity:
Local governments are often better positioned to understand the needs of their communities due to their proximity to the people. They can devise and implement policies more efficiently and effectively, as they have a better understanding of the local context. In some cases, central governments may delegate certain tasks to local governments to ensure that policies are tailored to local needs and implemented more efficiently.

5. Overburdened Central Government:
If the central government is overwhelmed with numerous responsibilities or lacks the capacity to handle certain tasks, it may delegate some of its work to local governments. This can help alleviate the workload of the central government and ensure that services are delivered more effectively. However, it is crucial to strike a balance and ensure that local governments have the necessary resources and capacity to carry out these additional responsibilities.

In summary, local governments can take on central government work through devolution, decentralization, addressing regional disparities, leveraging efficiency and proximity, and relieving the burden on the central government. This allows for better governance, improved service delivery, and tailored policies that meet the specific needs of local communities.