'being fired' is a noun (specifically, a gerundival phrase) so it needs an adjective. Both your and you belong to the class Pronoun. you, if we put it in your example, would function as an object pronoun (for example, the ungrammatical: I confirm that this meeting has resulted in him being given. It should be, 'his being given'). your, on the other hand, is a possessive pronoun. It functions as an adjective. That is, it modifies nouns.
Note that, some speakers and writers incorrectly use the object pronoun (me, you, her, him, them) instead of the possessive pronoun (my, your, her, his, their). That is, we hear and read both, so when it comes to using a gerund, we're not sure which pronoun to use. Use the adjective.
Thank you both: my sister and I have had a very interesting discussion following your posts! I am now registered on this forum (had to ask the question as an 'unregistered being' as my sister insisted it was asked immediately).