She ended up (being??) a rich woman

Solution 1:

End up is an idiom meaning 'come finally to (some situation or conclusion)' and can take a gerund complement describing the end state, which can be a predicate adjective or noun (with a being auxiliary). It has pretty much the same meaning and grammar as wind up.

• She ended up going to the movies after all.
• She ended up writing about her mother.
• She ended up being bored out of her skull.
• She ended up being too weak to stand.
• She ended up being the assistant producer.

Auxiliary forms of be can be deleted by many rules, since they're predictable, so Whiz-deletion and to be-deletion are common in relative clauses and infinitive complements. This also happens to being auxiliaries with end up:

• the man who was standing on the corner ==> the man standing on the corner
  (Whiz-deletion)
• He's considered to be lazy ==> He's considered lazy
  (to be-deletion)
• She ended up being a country lawyer ==> She ended up a country lawyer.
  (being-deletion)