So ambiguous...this can be translated to her/their/your eggs. In spoken German, do such issues exist, or does context help greatly in understanding?
context helps greatly. If you are talking about some 3rd person, you introduced that person before using the pronoun. And if you address someone and you use then sentences with "Sie" (e.g. "Sie gehen besser nach Hause.") you refer to the addresse and no unintroduced 3rd person plural.