• Ellipsis
• Minor Sentence
• Verbless Sentence

Examples and Observations:

• Generic drugs must be chosen when available or an additional expense will be incurred.
• Although not unfriendly toward strangers, this dog will protect its family in times of danger.

• "Verbless clauses are clauses in which the verb (usually a form of to be) and sometimes other elements have been deleted. Consider, for example:

  (36) John believes the prisoner innocent.

  In this sentence the italicized sequence is a verbless clause, which we assume is a reduced version of the to-infinitive clause (37):

  (37) John believes the prisoner to be innocent.

  The following sentences contain further examples of verbless clauses (italicized):

  (38) He considered the girl a good student.
  (39) Whenever in trouble, Bill rang his girl-friend.
  (40) He married her when a student at Harvard.

  (Herman Wekker and Liliane M. V. Haegeman, A Modern Course in English Syntax. Taylor & Francis, 1985)
• "Verbless clauses are clauses which contain no verb element, and often also no subject. They are regarded as clauses because they function in ways which make them equivalent to finite and non-finite clauses, and because they can be analyzed in terms of one or more clause elements."
  (Geoffroy Leech and Jan Svartvik, A Communicative Grammar of English, 1975)

• "A verbless clause . . . is considered a clause because it is dealing with a separate piece of information in relation to the main clause. For example, in the sentence, In the interests of the local children, the council should reconsider its decision, there are two separate pieces of information: the main clause--the council should reconsider its decision; and a dependent clause that deals with issues that interest local children. In this clause, however, the verb has been nominalised resulting in a verbless clause. Verbless clauses are different from adverbial phrases. The latter provide some information to do with the time, place, or manner in which something happens within an existing clause. Verbless clauses, on the other hand, provide a separate piece of information outside of an existing clause."
  (Peter Knapp and Megan Watkins, Genre, Text, Grammar: Technologies for Teaching and Assessing Writing. UNSW Press, 2005)