If a law firm only has one lawyer what happens to legal documents if that lawyer dies?

Trust paperwork you can keep a copy yourself.  Not really following how this is an issue.

The lawyer makes arrangements about all of his legal documents before his death.

I don't know about wherever you are but here the Solicitors Regulation Authority will go to the late lawyer's office and take all documents and papers that relate to his clients, including files and accounting records. They keep the documents safe and, if appropriate, return them to the people they belong to. They also take all money held by the firm, including its clients' money, and likewise keep it safe to deliver to whoever it belongs to.  Doubtless there is something similar there.

You could, of course, actually ask the lawyer in question . . . 

If a law firm has only one attorney, and that attorney passes, what I have see occur is:  Other lawyers that practice in that same county usually come to the decedent lawyer’s offices, and they divide up the files/work/documents between them.   However, usually an older attorney will have a younger attorney working with them - in a case like this, the younger attorney takes over the files/documents.   

Like Drs most lawyers in private practice sell their practice when death is pending
If its an unexpected death the heirs get custody at which time you hire another lawyer to request your files.
But as others have pointed out you will have a copy so even if the lawyers files were destroyed or lost it wouldn't matter

You would hold copies of the paperwork as well.  

What SHOULD happen is that the lawyer has an arrangement with another lawyer, or with the county law association, so that a second lawyer can take over. But occasionally (rarely) this fails, and the clients have to go to a lot of trouble to do things over again.

Personally, I would worry more about a herd of pink Martian elephants trashing the lawyers office.

There is a process in each state. Active documents are turned over to the family members or another lawyer/relevant party.