It can be either one, really. In English we'd differentiate: "What is your guys' job?" would imply the speaker knows they are a team and should be working together.
"What are your guys' jobs?" would sort of be small talk to a larger group.
Without that context how can we know what to write accept to just learn the 'right' answer; which certainly shouldn't be the point.
This is actually an eclipse, not a lenition. And, yes, if the starting letter can be eclipsed, it does occur.
It could mean “your post” in the sense of the service provided by a delivery organization, rather than “your mail” in the sense of items delivered through such a service. It could also mean “your (wooden) post”.