Also, do you have plans to support deletion of indexed data?
So Kite should be able to avoid this fear by asking only for limited license. For example, a license can expire after 1 year, or be untransferable (or perhaps expire at bankruptcy?).
Facebook does this to some extent: "This IP License ends when you delete your IP content or your account unless your content has been shared with others, and they have not deleted it."
Here's what Heroku does: "Heroku claims no ownership or control over any Content or Application. You retain copyright and any other rights you already hold in the Content and/or Application, and you are responsible for protecting those rights, as appropriate. By submitting, posting or displaying the Content on or through the Heroku Services you give Heroku a worldwide, royalty-free, and non-exclusive license to reproduce, adapt, modify, translate, publish, publicly perform, publicly display and distribute such Content for the sole purpose of enabling Heroku to provide you with the Heroku Services. [...]"
(IANAL)
A lot of companies' privacy policies have a section explicitly dealing with how data is transferred when company ownership changes. Sometimes this just says that all data will be transferred, but sometimes there are stipulations (for instance, my company doesn't sell or rent user data for marketing purposes, and its privacy policy requires that an acquiring company won't do that either).
Of course, there are edge cases (like what happens if the privacy policy changes) that complicate things, but the FTC has a pretty helpful discussion of all of this: https://www.ftc.gov/news-events/blogs/business-blog/2015/03/...
Some technical solutions might be possible, in terms of allowing users provably to withdraw their data, but it would be messy and probably not bulletproof.