However, after the page is rendered, I don't see the value attribute being rendered. So I wanted to know why it is not being rendered?
Because it's not relevant in order to trigger a Boolean. Just the request parameter being null or non-null depending on HTML checked state is sufficient to represent a Boolean. The <h:selectBooleanCheckbox> doesn't support non-Boolean values anyway.
If you're absolutely positive you need a checkbox value, use either <h:selectManyCheckbox> with only a single item.
<h:selectManyCheckbox value="#{bean.selectedValues}">
<f:selectItem itemValue="#{bean.someValue}" itemLabel="#{null}" />
</h:selectManyCheckbox>
Or if it's actually for JavaScript purposes (I'm just guessing because you confusingly tagged javascript on a JSF question without explaining its relevance anywhere), then you could also use a HTML5 data attribute which you can set as passthrough attribute (requires JSF 2.2).
<html ... xmlns:a="http://xmlns.jcp.org/jsf/passthrough">
...
<h:selectBooleanCheckbox value="#{bean.someBoolean}" a:data-value="#{bean.someValue}" />
It'll be available in JS as below:
var value = element.dataset.value;
Or jQuery:
var value = $(element).data("value");
See also: