Tumblr enables users to share content by reblogging it on their own blogs with the click of a button. This process can help spread a photo or post to a much larger audience. If you decide to delete your Tumblr blog or account, all your content is removed. However, this doesn't mean any posts that others have reblogged from you are deleted with it.
How Deletion Works on Tumblr
Tumblr blogs fall under one of two types: primary and secondary. A primary blog URL is created as soon as you sign up with Tumblr, and under this blog you can create as many secondary blogs as you like. You can delete secondary blogs without affecting any other blogs on your account, but if you delete your primary blog it will take all secondary blogs with it. All posts and content associated with the blog are deleted, and Tumblr can't restore or reactivate blogs or content later. Anything you have reblogged from others is deleted along with your content.
How Reblogs Work
Reblogging on Tumblr is similar to retweeting on Twitter. The original message is untouched, but you are essentially copying it to repost to your own account. When you reblog something, the new post will show the content's original source, as well as where you reblogged it from. To reblog a post, click on the small icon that looks like two arrows pointing in opposite directions. You'll have the option to alter the post before you click "Reblog."
Original Deleted, Copies Remain
Because a reblogged post is essentially a copy, deleting the original post will not affect reblogs of it. If you delete the blog or entire account where the original post resided, all reblogs of that post still remain and can continue being reblogged indefinitely. Once a post is reblogged, it has essentially taken on a life of its own -- it can spread throughout Tumblr and even to other social networks such as Facebook and Twitter.
Remove All Traces
In most cases, a reblogged post shouldn't pose much of an issue if you decide to delete your blog or account. However, you have very limited recourse to have reblogs completely removed. You could try contacting all the Tumblr users who have reblogged it and ask them to delete the reblog from their accounts, or seek help through Tumblr's customer support. Neither option is foolproof, however, and you may never completely erase all traces of your deleted content.