Husband abandons razor perhaps that preserves his dignity? (4-5)
I believe the answer is:
Here is my best explanation:
'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" and "Preserver of one's dignity".)