diff --git a/src/Type/Generic/TemplateBenevolentUnionType.php b/src/Type/Generic/TemplateBenevolentUnionType.php
index c8c2caaefdf..d9e1a100267 100644
--- a/src/Type/Generic/TemplateBenevolentUnionType.php
+++ b/src/Type/Generic/TemplateBenevolentUnionType.php
@@ -3,6 +3,7 @@
 namespace PHPStan\Type\Generic;
 
 use PHPStan\Type\BenevolentUnionType;
+use PHPStan\Type\NeverType;
 use PHPStan\Type\Type;
 
 /** @api */
@@ -50,6 +51,9 @@ public function withTypes(array $types): self
 	public function filterTypes(callable $filterCb): Type
 	{
 		$result = parent::filterTypes($filterCb);
+		if ($result instanceof NeverType) {
+			return $result;
+		}
 		if (!$result instanceof TemplateType) {
 			return TemplateTypeFactory::create(
 				$this->getScope(),
diff --git a/src/Type/Generic/TemplateUnionType.php b/src/Type/Generic/TemplateUnionType.php
index dc58af565aa..6a9e7f49477 100644
--- a/src/Type/Generic/TemplateUnionType.php
+++ b/src/Type/Generic/TemplateUnionType.php
@@ -2,6 +2,7 @@
 
 namespace PHPStan\Type\Generic;
 
+use PHPStan\Type\NeverType;
 use PHPStan\Type\Type;
 use PHPStan\Type\UnionType;
 
@@ -37,6 +38,9 @@ public function __construct(
 	public function filterTypes(callable $filterCb): Type
 	{
 		$result = parent::filterTypes($filterCb);
+		if ($result instanceof NeverType) {
+			return $result;
+		}
 		if (!$result instanceof TemplateType) {
 			return TemplateTypeFactory::create(
 				$this->getScope(),
diff --git a/tests/PHPStan/Rules/Pure/PureFunctionRuleTest.php b/tests/PHPStan/Rules/Pure/PureFunctionRuleTest.php
index 9ae7657ddbc..9fa246f5552 100644
--- a/tests/PHPStan/Rules/Pure/PureFunctionRuleTest.php
+++ b/tests/PHPStan/Rules/Pure/PureFunctionRuleTest.php
@@ -209,4 +209,9 @@ public function testBug12119(): void
 		$this->analyse([__DIR__ . '/data/bug-12119.php'], []);
 	}
 
+	public function testBug14504(): void
+	{
+		$this->analyse([__DIR__ . '/data/bug-14504.php'], []);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Pure/PureMethodRuleTest.php b/tests/PHPStan/Rules/Pure/PureMethodRuleTest.php
index 7a6a0ae9f57..2b896c17b10 100644
--- a/tests/PHPStan/Rules/Pure/PureMethodRuleTest.php
+++ b/tests/PHPStan/Rules/Pure/PureMethodRuleTest.php
@@ -377,4 +377,10 @@ public function testBug12382(): void
 		]);
 	}
 
+	public function testBug14504(): void
+	{
+		$this->treatPhpDocTypesAsCertain = true;
+		$this->analyse([__DIR__ . '/data/bug-14504-method.php'], []);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Pure/data/bug-14504-method.php b/tests/PHPStan/Rules/Pure/data/bug-14504-method.php
new file mode 100644
index 00000000000..acbd43de8e4
--- /dev/null
+++ b/tests/PHPStan/Rules/Pure/data/bug-14504-method.php
@@ -0,0 +1,19 @@
+<?php declare(strict_types = 1);
+
+namespace Bug14504Method;
+
+/**
+ * @template T of int|string
+ */
+class Foo
+{
+
+	/** @param T $val */
+	public function __construct(private $val) {}
+
+	/** @phpstan-pure */
+	public function toString(): string {
+		return (string)$this->val;
+	}
+
+}
diff --git a/tests/PHPStan/Rules/Pure/data/bug-14504.php b/tests/PHPStan/Rules/Pure/data/bug-14504.php
new file mode 100644
index 00000000000..f4192a3c314
--- /dev/null
+++ b/tests/PHPStan/Rules/Pure/data/bug-14504.php
@@ -0,0 +1,43 @@
+<?php declare(strict_types = 1);
+
+namespace Bug14504;
+
+/**
+ * @phpstan-pure
+ * @template T of int|string
+ * @param T $val
+ * @return string
+ */
+function stringCast($val): string {
+	return (string)$val;
+}
+
+/**
+ * @phpstan-pure
+ * @template T of int|string
+ * @param T $val
+ * @return string
+ */
+function stringConcat($val): string {
+	return '' . $val;
+}
+
+/**
+ * @phpstan-pure
+ * @template T of int|string
+ * @param T $val
+ * @return string
+ */
+function stringInterpolation($val): string {
+	return "$val";
+}
+
+/**
+ * @phpstan-pure
+ * @template T of int|float|bool
+ * @param T $val
+ * @return string
+ */
+function nonStringNonObjectCast($val): string {
+	return (string)$val;
+}