To answer your question directly, the two values are multiplied together and result in "0" value for all pixels in the emission channel.

Some more in depth thoughts on the subject:

Multiplication

To start with, the color in the texture map gets multiplied by the number value, and each resulting pixel then has that color value in the emission channel. So if you have a texture that is all black (0,0,0) and you have a strength value of 10 you still get no light out of it because 10x0=0. Likewise, if you have any color texture map loaded and a strength of 0, the result will also be all black and thus not cast any light.

HDR

If you are using deferred render path and have an HDR camera, this allows your color channels to exceed the range 0.0-1.0. So it is possible to have an object with a value of (5.0, 0.0, 0.0) being emitted from a pixel or pixels. Now when this gets composited to the screen, it gets clamped to (1.0, 0.0, 0.0) but with camera effects like Bloom, you can use this "over-value" as a parameter to determine how much bloom to apply in that area of the screen. This will work for both static and dynamic objects.

Convergence

If you have a non-primary color, like orange (1.0, 0.5, 0.0) and a strength of 2, that actually represents (2.0, 1.0, 0.0) and when that composites to the screen, it will clamp to (1.0, 1.0, 0.0), but your bloom filter could still have an orange halo - this actually is a great effect. So any non-primary color emission will converge toward white the more over-driven it is.

Static light mapping

Specifically for static objects (because of baked lighting), emissive texture regions will cast light on other static objects in the light map, so this is another useful element - this is how you make ceiling lights cast a natural glow on a hallway for example, or a computer screen light up the surrounding area.