diff --git a/fuzz/qpdf_extra/16172.fuzz b/fuzz/qpdf_extra/16172.fuzz
new file mode 100644
index 00000000..47f6cbcd
--- /dev/null
+++ b/fuzz/qpdf_extra/16172.fuzz
@@ -0,0 +1 @@
+  ÿ%PDF-1.4startxref 9223372036854775805
\ No newline at end of file
diff --git a/libqpdf/OffsetInputSource.cc b/libqpdf/OffsetInputSource.cc
index 2923c388..b6dae255 100644
--- a/libqpdf/OffsetInputSource.cc
+++ b/libqpdf/OffsetInputSource.cc
@@ -1,10 +1,20 @@
 #include <qpdf/OffsetInputSource.hh>
+#include <limits>
+#include <sstream>
+#include <stdexcept>
 
 OffsetInputSource::OffsetInputSource(PointerHolder<InputSource> proxied,
                                      qpdf_offset_t global_offset) :
     proxied(proxied),
     global_offset(global_offset)
 {
+    if (global_offset < 0)
+    {
+        throw std::logic_error(
+            "OffsetInputSource constructed with negative offset");
+    }
+    this->max_safe_offset =
+        std::numeric_limits<qpdf_offset_t>::max() - global_offset;
 }
 
 OffsetInputSource::~OffsetInputSource()
@@ -34,12 +44,25 @@ OffsetInputSource::seek(qpdf_offset_t offset, int whence)
 {
     if (whence == SEEK_SET)
     {
+        if (offset > this->max_safe_offset)
+        {
+            std::ostringstream msg;
+            msg << "seeking to " << offset
+                << " offset by " << global_offset
+                << " would cause an overflow of the offset type";
+            throw std::range_error(msg.str());
+        }
         this->proxied->seek(offset + global_offset, whence);
     }
     else
     {
         this->proxied->seek(offset, whence);
     }
+    if (tell() < 0)
+    {
+        throw std::runtime_error(
+            "offset input source: seek before beginning of file");
+    }
 }
 
 void
diff --git a/libqpdf/qpdf/OffsetInputSource.hh b/libqpdf/qpdf/OffsetInputSource.hh
index d541db1a..fef23760 100644
--- a/libqpdf/qpdf/OffsetInputSource.hh
+++ b/libqpdf/qpdf/OffsetInputSource.hh
@@ -24,6 +24,7 @@ class OffsetInputSource: public InputSource
   private:
     PointerHolder<InputSource> proxied;
     qpdf_offset_t global_offset;
+    qpdf_offset_t max_safe_offset;
 };
 
 #endif // QPDF_OFFSETINPUTSOURCE_HH