What do you mean by REST? Let's suppose, we refer to Roy Fielding and Http 1.1 standard.
According to standard, DELETE is idempotent method. I.e. if you request DELETE more than once, side-effects would be the same. I.e. all the same record in DB would be marked as "deleted" or be absent.
First of all, to request DELETE, you request a resource. Say, http://some.url/to/resource. If it never was present - you should respond with 404.
Section "9.7 DELETE" of the standard says:
A successful response SHOULD be 200 (OK) if the response includes an
entity describing the status, 202 (Accepted) if the action has not
yet been enacted, or 204 (No Content) if the action has been enacted
but the response does not include an entity.
If you don't remove a record completely from DB and want to communicate on subsequent requests that resource had been deleted and is no longer available, then the standard, section "10.4.11 410 Gone", says:
The 410 response is primarily intended to assist the task of web
maintenance by notifying the recipient that the resource is
intentionally unavailable and that the server owners desire that
remote links to that resource be removed.
But using this response code or providing it for some time period is not necessary, and response could be also 404. So use it, if you want to differentiate, whether a resource had been deleted or had never been present.