diff --git a/DependencyInjection/CachePoolPass.php b/DependencyInjection/CachePoolPass.php
index b4d77fd7..1a857647 100644
--- a/DependencyInjection/CachePoolPass.php
+++ b/DependencyInjection/CachePoolPass.php
@@ -55,9 +55,11 @@ public function process(ContainerBuilder $container): void
                 continue;
             }
             $class = $adapter->getClass();
+            $providers = $adapter->getArguments();
             while ($adapter instanceof ChildDefinition) {
                 $adapter = $container->findDefinition($adapter->getParent());
                 $class = $class ?: $adapter->getClass();
+                $providers += $adapter->getArguments();
                 if ($t = $adapter->getTag('cache.pool')) {
                     $tags[0] += $t[0];
                 }
@@ -87,7 +89,7 @@ public function process(ContainerBuilder $container): void
 
             if (ChainAdapter::class === $class) {
                 $adapters = [];
-                foreach ($adapter->getArgument(0) as $provider => $adapter) {
+                foreach ($providers['index_0'] ?? $providers[0] as $provider => $adapter) {
                     if ($adapter instanceof ChildDefinition) {
                         $chainedPool = $adapter;
                     } else {
diff --git a/Tests/DataCollector/CacheDataCollectorTest.php b/Tests/DataCollector/CacheDataCollectorTest.php
index cea761f5..e2cebc77 100644
--- a/Tests/DataCollector/CacheDataCollectorTest.php
+++ b/Tests/DataCollector/CacheDataCollectorTest.php
@@ -120,9 +120,9 @@ public function testLateCollect()
 
         $stats = $collector->getStatistics();
         $this->assertGreaterThan(0, $stats[self::INSTANCE_NAME]['time']);
-        $this->assertEquals($stats[self::INSTANCE_NAME]['hits'], 0, 'hits');
-        $this->assertEquals($stats[self::INSTANCE_NAME]['misses'], 1, 'misses');
-        $this->assertEquals($stats[self::INSTANCE_NAME]['calls'], 1, 'calls');
+        $this->assertEquals(0, $stats[self::INSTANCE_NAME]['hits'], 'hits');
+        $this->assertEquals(1, $stats[self::INSTANCE_NAME]['misses'], 'misses');
+        $this->assertEquals(1, $stats[self::INSTANCE_NAME]['calls'], 'calls');
         $this->assertInstanceOf(Data::class, $collector->getCalls());
     }
 
diff --git a/Tests/DependencyInjection/CachePoolPassTest.php b/Tests/DependencyInjection/CachePoolPassTest.php
index ef64d193..6527ccef 100644
--- a/Tests/DependencyInjection/CachePoolPassTest.php
+++ b/Tests/DependencyInjection/CachePoolPassTest.php
@@ -209,7 +209,8 @@ public function testChainAdapterPool()
         $container->register('cache.adapter.apcu', ApcuAdapter::class)
             ->setArguments([null, 0, null])
             ->addTag('cache.pool');
-        $container->register('cache.chain', ChainAdapter::class)
+        $container->register('cache.adapter.chain', ChainAdapter::class);
+        $container->setDefinition('cache.chain', new ChildDefinition('cache.adapter.chain'))
             ->addArgument(['cache.adapter.array', 'cache.adapter.apcu'])
             ->addTag('cache.pool');
         $container->setDefinition('cache.app', new ChildDefinition('cache.chain'))
@@ -224,7 +225,7 @@ public function testChainAdapterPool()
         $this->assertSame('cache.chain', $appCachePool->getParent());
 
         $chainCachePool = $container->getDefinition('cache.chain');
-        $this->assertNotInstanceOf(ChildDefinition::class, $chainCachePool);
+        $this->assertInstanceOf(ChildDefinition::class, $chainCachePool);
         $this->assertCount(2, $chainCachePool->getArgument(0));
         $this->assertInstanceOf(ChildDefinition::class, $chainCachePool->getArgument(0)[0]);
         $this->assertSame('cache.adapter.array', $chainCachePool->getArgument(0)[0]->getParent());
diff --git a/Traits/Relay/BgsaveTrait.php b/Traits/Relay/BgsaveTrait.php
new file mode 100644
index 00000000..367f82f7
--- /dev/null
+++ b/Traits/Relay/BgsaveTrait.php
@@ -0,0 +1,36 @@
+<?php
+
+/*
+ * This file is part of the Symfony package.
+ *
+ * (c) Fabien Potencier <fabien@symfony.com>
+ *
+ * For the full copyright and license information, please view the LICENSE
+ * file that was distributed with this source code.
+ */
+
+namespace Symfony\Component\Cache\Traits\Relay;
+
+if (version_compare(phpversion('relay'), '0.11', '>=')) {
+    /**
+     * @internal
+     */
+    trait BgsaveTrait
+    {
+        public function bgsave($arg = null): \Relay\Relay|bool
+        {
+            return ($this->lazyObjectState->realInstance ??= ($this->lazyObjectState->initializer)())->bgsave(...\func_get_args());
+        }
+    }
+} else {
+    /**
+     * @internal
+     */
+    trait BgsaveTrait
+    {
+        public function bgsave($schedule = false): \Relay\Relay|bool
+        {
+            return ($this->lazyObjectState->realInstance ??= ($this->lazyObjectState->initializer)())->bgsave(...\func_get_args());
+        }
+    }
+}
diff --git a/Traits/RelayProxy.php b/Traits/RelayProxy.php
index e0ca8873..b6d48dd5 100644
--- a/Traits/RelayProxy.php
+++ b/Traits/RelayProxy.php
@@ -11,6 +11,7 @@
 
 namespace Symfony\Component\Cache\Traits;
 
+use Symfony\Component\Cache\Traits\Relay\BgsaveTrait;
 use Symfony\Component\Cache\Traits\Relay\CopyTrait;
 use Symfony\Component\Cache\Traits\Relay\GeosearchTrait;
 use Symfony\Component\Cache\Traits\Relay\GetrangeTrait;
@@ -31,6 +32,7 @@ class_exists(\Symfony\Component\VarExporter\Internal\LazyObjectState::class);
  */
 class RelayProxy extends \Relay\Relay implements ResetInterface, LazyObjectInterface
 {
+    use BgsaveTrait;
     use CopyTrait;
     use GeosearchTrait;
     use GetrangeTrait;
@@ -338,11 +340,6 @@ public function lcs($key1, $key2, $options = null): mixed
         return $this->initializeLazyObject()->lcs(...\func_get_args());
     }
 
-    public function bgsave($schedule = false): \Relay\Relay|bool
-    {
-        return $this->initializeLazyObject()->bgsave(...\func_get_args());
-    }
-
     public function save(): \Relay\Relay|bool
     {
         return $this->initializeLazyObject()->save(...\func_get_args());