I think this is a very complicated question, but to put it very basically, it depends on the absoluteness of the state expressed by the adjective. If you're talking about temporary, transient emotional states, for example, you can more easily get away with omitting the verb. Conversely, for more permanent states, the verb must be retained.
Being single, you don't qualify for tax relief.
Being dead, he can't exactly object, can he?
You can't omit 'being' in these sentences since the states have a sense of permanence.
Disappointed, she quietly left without saying a word.
Dazed and confused, he staggered into Stoneham Park.
Here, the verb can easily be dropped since the states are more transient.
An equally relevant point is that dropping the verb has a particularly narrative style. We don't really do it outside of written narratives, such as novels and short stories.
