There is only one subject, her "nature", so "doesn't" is correct.
It is the adjectives "hard-working" and "honest" that are joined by "and".
not a teacher
"Her hard-working and honest nature will not save her from bearing the brunt of drastic cuts targeted at the benefits system."(c) When two or more subjects are joined by “and” and refer to the same person or thing, the verb is in the singular. However, compound subjects referring to two different people or things take plural verbs.
Examples:(i) His brother and sponsor was there to help him.
(ii) The President and Commander-in-chief of the Armed Forces has arrived.(iii) A dog and a cat are seldom friends.
(iv) The man and his wife have arrived.
More: GRAMMAR Part 2: Subject-Verb Agreement (Concord) | Faith Brown
Can I construct the underlined part in the present simple tense using the verb in singular?
Example:
Her hard-working and honest nature doesn't save her ....
Question: Does this sentence satisfy what has been mentioned in the blue-colored statement?
There is only one subject, her "nature", so "doesn't" is correct.
It is the adjectives "hard-working" and "honest" that are joined by "and".
not a teacher
Grateful to you, JMurray. To be honest, I always thought that hard-working was a noun, how wrong I was? Anyhow, does the following sentence make sense?
Her hard work and honest nature doesn't save her ....
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.
Here are two subjects joined by "and" and referring to the same person, taking a singular verb.
"This hard worker and honest employee is not saved by her good character."
not a teacher