diff --git a/x-pack/plugin/ml/qa/native-multi-node-tests/src/test/java/org/elasticsearch/xpack/ml/integration/RegressionIT.java b/x-pack/plugin/ml/qa/native-multi-node-tests/src/test/java/org/elasticsearch/xpack/ml/integration/RegressionIT.java
index 777451baca7a9..5ecab6f69d429 100644
--- a/x-pack/plugin/ml/qa/native-multi-node-tests/src/test/java/org/elasticsearch/xpack/ml/integration/RegressionIT.java
+++ b/x-pack/plugin/ml/qa/native-multi-node-tests/src/test/java/org/elasticsearch/xpack/ml/integration/RegressionIT.java
@@ -183,7 +183,6 @@ public void testWithOnlyTrainingRowsAndTrainingPercentIsFifty() throws Exception
             "Finished analysis");
     }
 
-    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/49680")
     public void testStopAndRestart() throws Exception {
         initialize("regression_stop_and_restart");
         indexData(sourceIndex, 350, 0);
diff --git a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/process/AbstractNativeProcess.java b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/process/AbstractNativeProcess.java
index 62c060de03a50..33c2dc5ac6ef6 100644
--- a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/process/AbstractNativeProcess.java
+++ b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/process/AbstractNativeProcess.java
@@ -30,6 +30,7 @@
 import java.util.concurrent.Future;
 import java.util.concurrent.TimeUnit;
 import java.util.concurrent.TimeoutException;
+import java.util.concurrent.atomic.AtomicBoolean;
 import java.util.function.Consumer;
 
 /**
@@ -44,6 +45,9 @@ public abstract class AbstractNativeProcess implements NativeProcess {
     private final String jobId;
     private final CppLogMessageHandler cppLogHandler;
     private final OutputStream processInStream;
+    // We need this as in Java 8 closing {@link FilterOutputStream} is not idempotent (i.e. cannot be performed twice).
+    // For more details regarding the underlying issue see https://bugs.openjdk.java.net/browse/JDK-8054565
+    private final AtomicBoolean processInStreamClosed = new AtomicBoolean();
     private final InputStream processOutStream;
     private final OutputStream processRestoreStream;
     private final LengthEncodedWriter recordWriter;
@@ -163,7 +167,10 @@ public void close() throws IOException {
             processCloseInitiated = true;
             // closing its input causes the process to exit
             if (processInStream != null) {
-                processInStream.close();
+                // Make sure {@code processInStream.close()} is called at most once.
+                if (processInStreamClosed.compareAndSet(false, true)) {
+                    processInStream.close();
+                }
             }
             // wait for the process to exit by waiting for end-of-file on the named pipe connected
             // to the state processor - it may take a long time for all the model state to be
@@ -209,7 +216,10 @@ public void kill() throws IOException {
         } finally {
             try {
                 if (processInStream != null) {
-                    processInStream.close();
+                    // Make sure {@code processInStream.close()} is called at most once.
+                    if (processInStreamClosed.compareAndSet(false, true)) {
+                        processInStream.close();
+                    }
                 }
             } catch (IOException e) {
                 // Ignore it - we're shutting down and the method itself has logged a warning