Are there warrants from 100 years ago? When do they assume the person dies? Does it go back to the digitization of records in the late seventies, or further back?
The question is twofold: how long a warrent is valid for execution and then it's archivation.
Validity of warrents for execution depends on the crime, the jurisdiction and even the legal system it is under.
In western countries of bother Code Civil and Common Law origin, warrants come generally with an expiration date. This is generally given by the statue of limitations. However, this deadline can be extended for different reasons, like fleeing to a different country (which halts the statue of limitations for some crimes). Also note that some crimes, like murder, gave no statue of limitations.
Shari'ah law has also a similar concept for the validity of claims, requiring for example that witnesses for adultery or theft need to come forth within a month of the act or the suit is dismissed. For drinking alcohol, the offender needs to still be drunk or reek of the stuff in the presence of a judge (making that possiblity the shortest statue of limitations possible with about 8-16 hours).
However, (physical) warrants issued by the court are also court documents. As such, they are to be archived and kept for posterity, for example to review the legal process. While they might be digitalized, access to them might be restricted due to privacy laws.