A famous scholar sent me an unpublished draft of hers. Then she died. I think her work should be published. What should I do?
The first thing to do is to contact her estate. You can probably reach someone through her last affiliation. I assume that they have control over all of the papers and effects of the deceased. 

Since you say she is famous, there my be some posthumous attempt to honor her in some collected publication, but the estate, possibly a spouse, should have knowledge of that. Her last employer might also. 

But start there. 

And, of course it is possible that it has already been submitted somewhere and publication is in process. The estate might even welcome contact with interested people in finalizing publication as needed.