Usually they just keep your name, contact details, what publications they've left you and maybe a few personal details (children, hobbies/interests, notable personal problems, etc)
The only reason I can think of for passing it on is if they couldn't do the study anymore, in which case they'll give it to whoever takes over.
Do you mind if I ask what lead to your accepting a study? Do you have other jw family or aquaintences?
If you're interested, the site jwfacts.com has lots of information on jws, and what they currently teach, as well as what they've taught in the past. As a currently active jw, I found that website quite eye-opening and to be completely accurate.