Husband abandons razor perhaps that preserves his dignity? (4-5)

I believe the answer is:

face-saver

'that preserves his dignity?' is the definition.
(to save face is to preserve one's dignity)

I don't understand how the rest of the clue works.

(Other definitions for face-saver that I've seen before include "Something that maintains one's dignity" , "Preserver of one's dignity" .)

I've seen this clue in The Times.

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