Auxiliary verbs are also known as 'helping verbs'. They are used with the main verb to show the tense of the verb. The sentence is in past tense as the person is already unemployed. So, the blank in the given sentence would have something that has happened in the past. Use of options B and C which are 'To lose' and 'To be lost' respectively are grammatically incorrect. They both are in future tense.  Option D is ‘Losing’ which means losing something is in present tense. So, the best fit here is  option A 'Having lost'. 'Lost' is in past tense and the verb 'having' is used with it as a helping verb.