You don’t need to worry; your emails will remain safely in your email client. We don't store any of your emails on our servers.
Even after deleting your Unroll.Me account, the "Unroll.Me" and “Unroll.Me/Unsubscribed" labels will still show up in your mailbox. All of your previously rolled up and unsubscribed emails will remain in these folders.
Note: You can remove Unroll.Me's labels by accessing the settings on your email account. When you delete Unroll.Me's label, it only removes the label from your view options. It does not delete any messages that had the label assigned. Here you can find out how to delete labels in Gmail and Outlook.
Here is an image of the "Unroll.Me" and "Unroll.Me/Unsubscribed" folders in Gmail: