what is a phrase in linguistics?

I always understood that a minimal sentence was S+P (subject plus predicate). This is not specifically Bloomfield, and obviously S could be N or NP, P could be V or VP),

In fact googling "linguistics sentences" even yields the concept of a one word sentence, in the case of oral considerations.

In the sentence [he jumped]
both words are phrases unto themselves.
he = noun phrase jumped = verb phrase
s
/ \
NP VP
| |
he jumped

Thank you all for taking the trouble to answer the question. Now I see that I did not explain the question properly.
Let me tell you where the problem is.
I know for sure that 'he' and 'went' are phrases when they are in the sentence 'he went'. But my question is whether the word 'he' and 'went' standing independently of a sentence can get the status of a phrase since 'he' is the substitute of a larger unit 'the man' or some other construction of similar kind. What are the reasons?

I Hope, I have explained the question properly this time. English is my second language therefore, it takes time to write with clarity in the first attempt.

Yes Givon explains what he calls left shift, where the verb phrase shifts left, or right depending on the language's word order, but in English to the left. This is normally in the instances of commands and simple answers to questions. Others have argued that this turns the the represented word into a sentential proform.

So we have the sentence [sit] as in the comman you sit, and we have the sentence [him] as in the answer to the question (who said that?). Givon says that gramaticall the VP shifts left knocking the SP out of the picture, of course this requires quite a bit of deictic pre-knowledge. but in essense these also stand as pro-forms for the entire sentence (you sit) and (it was him). This would qualify for bloomfield's two morpheme minimum rule.