I faced this sentence actually:
One would be caught dead without one of these.
What does "would be caught dead" mean?
The fixed phrase is wouldn't be caught dead [in circumstance].
It means "would not allow oneself to be seen in this circumstance, even if you had the excuse of being dead". For example, "She wouldn't be caught dead without her high heels and shades". It means she always wore high heels and shades when in public.
Because the phrase is used a lot, it sometimes loses the negation, and "would be caught dead" means the identical thing to "wouldn't be caught dead". (In the same way as "could care less" means the same as "couldn't care less".)
Also, as a form of exaggerated understatement (litotes), you will occasionally see "I would be caught dead in" to mean "Absolute opposite of wouldn't be caught dead in". For example, someone at Pinterest lists her favourites as "Dresses I would be caught dead in :)"
Your example might be either of these second forms: without context it's impossible to tell.