As an experienced React developer, your understanding of core JavaScript concepts and React's lifecycle is crucial for building robust applications. This question explores your in-depth knowledge of JavaScript closures and their specific implications within React functional components.

Part 1: Define JavaScript Closures

Clearly explain what a JavaScript closure is. Your explanation should cover how a closure is formed, the essential components that constitute a closure, and its fundamental purpose in JavaScript programming. Provide a simple, non-React related JavaScript code example to illustrate your definition.

Part 2: Problem Description - Stale Closures in React's useEffect

Consider a React functional component with a state variable and an event listener attached within a useEffect hook. Describe a realistic scenario where an event handler, defined within this useEffect hook, might capture a 'stale' value of the state variable. Explain in detail why this happens, drawing a clear connection to JavaScript closures and the specific behavior of useEffect's closure mechanism over time. Discuss how React's re-rendering process interacts with useEffect to create this 'staleness'.

Part 3: Solution 1 - Utilizing the useEffect Dependency Array

Describe the first method to fix the stale closure problem identified in Part 2: correctly utilizing the useEffect dependency array. Explain how modifying the dependency array by including the state variable resolves the issue. Provide a conceptual code example or pseudocode demonstrating how this solution would be applied to the scenario described in Part 2, highlighting the changes to the useEffect hook and its dependencies.

Part 4: Solution 2 - Employing the useRef Hook

Describe an alternative method to fix the stale closure problem: employing the useRef hook. Explain the fundamental difference between useRef and state variables, specifically focusing on why useRef can store a mutable reference that persists across renders without triggering component re-renders. Illustrate how using useRef allows the event handler to always access the most current value of the state variable without requiring it in the useEffect dependency array. Provide a conceptual code example or pseudocode demonstrating how this solution would be applied to the scenario described in Part 2, showing the setup and usage of useRef.