Sure, here are a couple of unit tests for the given functional requirement using xUnit and Shouldly in C#:

```c#
using System;
using Xunit;
using Shouldly;

public class FibonacciTests
{
    [Fact]
    public void TestClosestFibonacciNumbersForNegativeNumber()
    {
        // Arrange
        double number = -10.5;

        // Act
        (int closest, int next) = Fibonacci.GetClosestFibonacciNumbers(number);

        // Assert
        closest.ShouldBe(0);
        next.ShouldBe(1);
    }

    [Fact]
    public void TestClosestFibonacciNumbersForLargeNumber()
    {
        // Arrange
        double number = 1000000;

        // Act
        (int closest, int next) = Fibonacci.GetClosestFibonacciNumbers(number);

        // Assert
        closest.ShouldBe(832040);
        next.ShouldBe(1346269);
    }
}
```

In this example, Fibonacci is the class that implements the algorithm to find the closest Fibonacci numbers.

The first test case checks whether the algorithm works correctly for negative input values. It expects the closest Fibonacci number to be 0 and the next one to be 1.

The second test case checks whether the algorithm works correctly for large input values. It expects the closest Fibonacci number to be 832040 and the next one to be 1346269.
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