diff --git a/src/Type/ValueOfType.php b/src/Type/ValueOfType.php
index d02b7d11f7..b8348dd84c 100644
--- a/src/Type/ValueOfType.php
+++ b/src/Type/ValueOfType.php
@@ -5,6 +5,7 @@
 use PHPStan\PhpDocParser\Ast\Type\GenericTypeNode;
 use PHPStan\PhpDocParser\Ast\Type\IdentifierTypeNode;
 use PHPStan\PhpDocParser\Ast\Type\TypeNode;
+use PHPStan\Type\Generic\TemplateType;
 use PHPStan\Type\Generic\TemplateTypeVariance;
 use PHPStan\Type\Traits\LateResolvableTypeTrait;
 use PHPStan\Type\Traits\NonGeneralizableTypeTrait;
@@ -50,8 +51,17 @@ public function isResolvable(): bool
 	protected function getResult(): Type
 	{
 		if ($this->type->isEnum()->yes()) {
+			$enumCases = $this->type->getEnumCases();
+			if (
+				$enumCases === []
+				&& $this->type instanceof TemplateType
+				&& (new ObjectType('BackedEnum'))->isSuperTypeOf($this->type->getBound())->yes()
+			) {
+				return new UnionType([new IntegerType(), new StringType()]);
+			}
+
 			$valueTypes = [];
-			foreach ($this->type->getEnumCases() as $enumCase) {
+			foreach ($enumCases as $enumCase) {
 				$valueType = $enumCase->getBackingValueType();
 				if ($valueType === null) {
 					continue;
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13282.php b/tests/PHPStan/Analyser/nsrt/bug-13282.php
new file mode 100644
index 0000000000..c8f06ce6df
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13282.php
@@ -0,0 +1,46 @@
+<?php // lint >= 8.1
+
+namespace Bug13283;
+
+use function PHPStan\Testing\assertType;
+
+enum Test: string
+{
+	case NAME = 'name';
+	case VALUE = 'value';
+}
+
+/**
+ * @template T of \BackedEnum
+ * @param class-string<T> $enum
+ * @phpstan-assert null|value-of<T> $value
+ */
+function assertValue(mixed $value, string $enum): void
+{
+	if (null === $value) {
+		return;
+	}
+
+	if (! is_int($value) && ! is_string($value)) {
+		throw new \Exception();
+	}
+
+	if (null === $enum::tryFrom($value)) {
+		throw new \Exception();
+	}
+}
+
+function getFromRequest(): mixed
+{
+	return 'name';
+}
+
+$v = getFromRequest();
+
+assertType('mixed', $v);
+
+assertValue($v, Test::class);
+
+assertType("'name'|'value'|null", $v);
+
+$a = null !== $v ? Test::from($v) : null;
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13782.php b/tests/PHPStan/Analyser/nsrt/bug-13782.php
new file mode 100644
index 0000000000..974ee51f11
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13782.php
@@ -0,0 +1,38 @@
+<?php // lint >= 8.1
+
+namespace Bug13782;
+
+use BackedEnum;
+use function PHPStan\Testing\assertType;
+
+enum IntEnum : int
+{
+	case A = 1;
+	case B = 2;
+}
+
+class EnumMethods
+{
+	/**
+	 * @template TEnum of BackedEnum
+	 * @param TEnum $enum
+	 * @return value-of<TEnum>
+	 */
+	public static function getValue(BackedEnum $enum): int|string
+	{
+		return $enum->value;
+	}
+
+	/**
+	 * @template TEnum of BackedEnum
+	 * @param TEnum|null $enum
+	 * @return ($enum is TEnum ? value-of<TEnum> : null)
+	 */
+	public static function getNullableValue(?BackedEnum $enum): int|string|null
+	{
+		return $enum === null ? null : $enum->value;
+	}
+}
+
+assertType("2", EnumMethods::getValue(IntEnum::B));
+assertType("2", EnumMethods::getNullableValue(IntEnum::B));
diff --git a/tests/PHPStan/Rules/Comparison/StrictComparisonOfDifferentTypesRuleTest.php b/tests/PHPStan/Rules/Comparison/StrictComparisonOfDifferentTypesRuleTest.php
index 9971f74981..965ed1e348 100644
--- a/tests/PHPStan/Rules/Comparison/StrictComparisonOfDifferentTypesRuleTest.php
+++ b/tests/PHPStan/Rules/Comparison/StrictComparisonOfDifferentTypesRuleTest.php
@@ -1034,6 +1034,12 @@ public function testBug13208(): void
 		$this->analyse([__DIR__ . '/data/bug-13208.php'], []);
 	}
 
+	#[RequiresPhp('>= 8.1')]
+	public function testBug13282(): void
+	{
+		$this->analyse([__DIR__ . '/../../Analyser/nsrt/bug-13282.php'], []);
+	}
+
 	public function testBug11609(): void
 	{
 		$this->analyse([__DIR__ . '/data/bug-11609.php'], [
diff --git a/tests/PHPStan/Rules/Functions/ReturnTypeRuleTest.php b/tests/PHPStan/Rules/Functions/ReturnTypeRuleTest.php
index c1fac8e311..169aff175f 100644
--- a/tests/PHPStan/Rules/Functions/ReturnTypeRuleTest.php
+++ b/tests/PHPStan/Rules/Functions/ReturnTypeRuleTest.php
@@ -357,6 +357,14 @@ public function testBug12274(): void
 		]);
 	}
 
+	#[RequiresPhp('>= 8.1')]
+	public function testBug13638(): void
+	{
+		$this->checkNullables = true;
+		$this->checkExplicitMixed = true;
+		$this->analyse([__DIR__ . '/data/bug-13638.php'], []);
+	}
+
 	public function testBug13484(): void
 	{
 		$this->checkExplicitMixed = true;
diff --git a/tests/PHPStan/Rules/Functions/data/bug-13638.php b/tests/PHPStan/Rules/Functions/data/bug-13638.php
new file mode 100644
index 0000000000..1951a78cc8
--- /dev/null
+++ b/tests/PHPStan/Rules/Functions/data/bug-13638.php
@@ -0,0 +1,15 @@
+<?php // lint >= 8.1
+
+namespace Bug13638;
+
+use BackedEnum;
+
+/**
+ * @template T of BackedEnum
+ * @param ?value-of<T> $a
+ * @return ($a is null ? list<?value-of<T>> : list<value-of<T>>)
+ */
+function test1(int | string | null $a): array
+{
+	return [$a];
+}
diff --git a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
index 0dbebf0da3..7eeeabb6fd 100644
--- a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
@@ -3666,6 +3666,16 @@ public function testBug3396(): void
 		$this->analyse([__DIR__ . '/data/bug-3396.php'], []);
 	}
 
+	#[RequiresPhp('>= 8.1')]
+	public function testBug12219(): void
+	{
+		$this->checkThisOnly = false;
+		$this->checkNullables = true;
+		$this->checkUnionTypes = true;
+		$this->checkExplicitMixed = true;
+		$this->analyse([__DIR__ . '/data/bug-12219.php'], []);
+	}
+
 	public function testBug13511(): void
 	{
 		$this->checkThisOnly = false;
diff --git a/tests/PHPStan/Rules/Methods/data/bug-12219.php b/tests/PHPStan/Rules/Methods/data/bug-12219.php
new file mode 100644
index 0000000000..85c52922c4
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-12219.php
@@ -0,0 +1,54 @@
+<?php // lint >= 8.1
+
+namespace Bug12219;
+
+class Bug
+{
+	/**
+	 * @template T of \BackedEnum
+	 * @param class-string<T> $class
+	 * @param value-of<T> $value
+	 */
+	public function foo(string $class, mixed $value): void
+	{
+	}
+
+	/**
+	 * @template Q of \BackedEnum
+	 * @param class-string<Q> $class
+	 * @param value-of<Q> $value
+	 */
+	public function bar(string $class, mixed $value): void
+	{
+		// Parameter #2 $value of static method Bug::foo() contains unresolvable type.
+		$this->foo($class, $value);
+	}
+}
+
+interface SuperBackedEnum extends \BackedEnum
+{
+	public function customMethod(): void;
+}
+
+class Bug2
+{
+	/**
+	 * @template T of SuperBackedEnum
+	 * @param class-string<T> $class
+	 * @param value-of<T> $value
+	 */
+	public function foo(string $class, mixed $value): void
+	{
+	}
+
+	/**
+	 * @template Q of SuperBackedEnum
+	 * @param class-string<Q> $class
+	 * @param value-of<Q> $value
+	 */
+	public function bar(string $class, mixed $value): void
+	{
+		// Parameter #2 $value of static method Bug::foo() contains unresolvable type.
+		$this->foo($class, $value);
+	}
+}