It depends on the theme itself. A theme may store some data in the database.
For example, a theme may have an option called “Social Accounts” section in settings page and a field “Facebook Page URL” in it. If you fill the field and save settings, it will store this value to database.
But, as a common practice, these type of data should be removed when you uninstall/delete this theme (it depends on the author). If it does not remove that data and you re-install the theme, then the values will be used again.