Hare in poor health close to exhaustion (3,3)

I believe the answer is:

run low

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'health close to exhaustion' is the definition.
I can't tell whether this definition defines the answer.

'hare in poor' is the wordplay.
'hare in' becomes 'run' (I can't justify this - if you can you should believe this answer much more).
'poor' becomes 'low' ('low' can be similar in meaning to 'poor').
'run'+'low'='RUN LOW'

Can you help me to learn more?

(Another definition for run low that I've seen is " Become depleted".)

I've seen this clue in The Guardian.

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