diff --git a/src/ifcopenshell-python/test/test_parse.py b/src/ifcopenshell-python/test/test_parse.py
index 992f842bf7..15de45fc29 100644
--- a/src/ifcopenshell-python/test/test_parse.py
+++ b/src/ifcopenshell-python/test/test_parse.py
@@ -1,3 +1,5 @@
+import math
+
 import ifcopenshell
 
 
@@ -21,7 +23,9 @@ END-ISO-10303-21;
 
 
 def test_reference_to_undefined_owning_instance():
-    data = "ISO-10303-21;HEADER;FILE_DESCRIPTION();FILE_NAME();FILE_SCHEMA(('IFC4'));#=IFCRELAGGREGATES((#))#5=IFCPOINT)"
+    data = (
+        "ISO-10303-21;HEADER;FILE_DESCRIPTION();FILE_NAME();FILE_SCHEMA(('IFC4'));#=IFCRELAGGREGATES((#))#5=IFCPOINT)"
+    )
     ifcopenshell.file.from_string(data)
     print(ifcopenshell.get_log())
 
@@ -30,3 +34,29 @@ def test_reference_to_undefined_owning_instance_simple_type():
     data = "ISO-10303-21;HEADER;FILE_DESCRIPTION();FILE_NAME();FILE_SCHEMA(('IFC4'));#=IFCPROJECT((#))#4=IFCSIUNIT("
     ifcopenshell.file.from_string(data)
     print(ifcopenshell.get_log())
+
+
+def test_non_finite_reals_with_trailing_dot():
+    # Legacy serialization appended '.' to non-finite doubles ("nan.", "inf."),
+    # which tokenized as unknown keywords and left zero-argument typed values
+    # that raised on attribute access (#6409).
+    data = """
+ISO-10303-21;
+HEADER;
+FILE_DESCRIPTION((''),'2;1');
+FILE_NAME('','',(''),(''),'','','');
+FILE_SCHEMA(('IFC2X3'));
+ENDSEC;
+DATA;
+#1=IFCPROPERTYSINGLEVALUE('test',$,IFCREAL(nan.),$);
+#2=IFCCARTESIANPOINT((0.,inf.,-inf.));
+#3=IFCDIRECTION((-nan.,-nan.,-nan.));
+ENDSEC;
+END-ISO-10303-21;
+"""
+    f = ifcopenshell.file.from_string(data)
+    log = ifcopenshell.get_log()
+    assert math.isnan(f.by_id(1).NominalValue.wrappedValue)
+    assert f.by_id(2).Coordinates == (0.0, math.inf, -math.inf)
+    assert all(math.isnan(ratio) for ratio in f.by_id(3).DirectionRatios)
+    assert "Non-finite value" in log
diff --git a/src/ifcparse/IfcParse.cpp b/src/ifcparse/IfcParse.cpp
index bc6df697af..1b7ed28bd3 100644
--- a/src/ifcparse/IfcParse.cpp
+++ b/src/ifcparse/IfcParse.cpp
@@ -30,6 +30,7 @@
 #include "utils.h"
 
 #include <algorithm>
+#include <cmath>
 #include <boost/algorithm/string.hpp>
 #include <boost/variant.hpp>
 #include <boost/math/special_functions/fpclassify.hpp>
@@ -283,7 +284,13 @@ bool ParseFloat(const char* pStart, double& val) {
     double result = strtod_l(pStart, &pEnd, locale);
 #endif
     if (*pEnd != 0) {
-        return false;
+        // Historically REALs were serialized by appending a '.' to any formatted
+        // double lacking one, producing non-finite spellings such as "nan.",
+        // "-nan(ind)." and "inf." that strtod stops in front of. Accept a single
+        // trailing '.' after a successful partial parse so these load again.
+        if (pEnd == pStart || pEnd[0] != '.' || pEnd[1] != 0) {
+            return false;
+        }
     }
     val = result;
     return true;
@@ -339,6 +346,9 @@ Token IfcParse::GeneralTokenPtr(IfcSpfLexer* lexer, size_t start, const std::str
         token.type = Token_INT;
     } else if (ParseFloat(tokenStr.c_str(), token.value_double)) {
         token.type = Token_FLOAT;
+        if (!std::isfinite(token.value_double)) {
+            lexer->logger().Message(Logger::LOG_ERROR, "SYN", 41, "Non-finite value '" + tokenStr + "' at offset " + std::to_string(token.startPos));
+        }
     } else {
         token.type = Token_KEYWORD;
     }