Problem : Node is created and deleted republished the entire site and search node not present in umbraco DB and umbraco.config  but still displaying in front end.

solution : Take backup of index folders and delete all the index folders and regenerate the index using:

1.Recycle app pool and Restart website.

If problem resolved no issue else go for next step 

2). publish the site from parent node of the culprit node with option (Publish "selected page" and all its subpages).

now check now culprit node will not appear in the front end.

My problem resolved 

Cheers,

Pushpendra Singh