If the deceased person made a will (i.e. died testate), the property interest in the documents, including any copyright interest, passes to the beneficiaries of the will. If there is no will, i.e. the person died intestate, then the property interest including any possible copyright claims, pass to the heirs as determined by the intestate statutes in the locality where the person died. You can see from this situation, that determining the true or correct ownership of any copyright claims could be really complicated and in some cases, likely impossible.
One of the questions that should be addressed is the age of the supposedly protected documents. The time limits for protection imposed by the copyright act do not go on forever, and it may well be that any claim for copyright protection has expired. A full discussion of the time limits that copyright claims survive is far too complicated to discuss in a blog post since the law has changed several times over the years. But if the documents are more than 100 years old, it is unlikely that any claim to copyright protection survives. If the documents are less than 100 years old, it is a good idea to carefully consider the applicable statutory provisions before making a decision as to whether the works are subject to some copyright protection or not. Here is the U.S. Copyright Office's explanation of the term of a copyright as it exists as of 2010 under the law:
The term of copyright for a particular work depends on several factors, including whether it has been published, and, if so, the date of first publication. As a general rule, for works created after January 1, 1978, copyright protection lasts for the life of the author plus an additional 70 years. For an anonymous work, a pseudonymous work, or a work made for hire, the copyright endures for a term of 95 years from the year of its first publication or a term of 120 years from the year of its creation, whichever expires first. For works first published prior to 1978, the term will vary depending on several factors. To determine the length of copyright protection for a particular work, consult chapter 3 of the Copyright Act (title 17 of the United States Code). More information on the term of copyright can be found in Circular 15a, Duration of Copyright, and Circular 1, Copyright Basics.
From a practical standpoint, the heirs of a deceased person rarely need to be concerned about copyright issues. The main exception to this rule is when the diary, journal or letters are commercially exploited. Then, the real copyright owners may have a claim for all or a portion of the income generated by the publication. The other area of concern, is if the documents reveal personal or private information about presently living individuals. Apart from any copyright issues, the people who are still living may have a basis for complaining about the publication based on privacy concerns.
Copyright concerns are a real issue and must be considered by anyone publishing anything either in physical format or online. If the present possessor of the documents is also the only heir to the deceased's estate, then the copyright would have passed to the possessor. If that is not the case, then the copyright is owned jointly by all of the heirs.