Your assumptions are exactly the opposite of what is really happening.
In the first scenario, you further enlarge your subject. The subject therefore covers more pixels on the same sensor because it occupies a larger part of the total area of the image. Since the number of pixels has not changed, your subject covers more, because it is larger than it is projected on the sensor.
In the second scenario, your subject covers the same number of pixels in the center of the sensor, but the area around your subject is now wider.
If you double the width and height of your sensor, you will quadruple the area and the number of pixels. 2,000 pixels in an area of 8 x 8 mm corresponds to 8,000 pixels in an area of 16 x 16 mm. But the size of the subject projected by the lens is the same, regardless of the size of the sensor. It just shows a wider angle of view.
There is a third scenario: keep the same lens and sensor size, but increase the pixel density so that there are more pixels in the same sensor area. This will increase the resolution of your subject if the limit of resolution of the lens had not already been exceeded by the resolution of the original sensor.