diff --git a/internal/jsonrpc2/conn.go b/internal/jsonrpc2/conn.go
index 4994c63b..5a2253b1 100644
--- a/internal/jsonrpc2/conn.go
+++ b/internal/jsonrpc2/conn.go
@@ -158,12 +158,12 @@ func (s *inFlightState) shuttingDown(errClosing error) error {
 	if s.readErr != nil {
 		// If the read side of the connection is broken, we cannot read new call
 		// requests, and cannot read responses to our outgoing calls.
-		return fmt.Errorf("%w: %v", errClosing, s.readErr)
+		return fmt.Errorf("%w: %w", errClosing, s.readErr)
 	}
 	if s.writeErr != nil {
 		// If the write side of the connection is broken, we cannot write responses
 		// for incoming calls, and cannot write requests for outgoing calls.
-		return fmt.Errorf("%w: %v", errClosing, s.writeErr)
+		return fmt.Errorf("%w: %w", errClosing, s.writeErr)
 	}
 	return nil
 }
@@ -671,7 +671,7 @@ func (c *Connection) handleAsync() {
 				if s.writeErr != nil {
 					// Assume that req.ctx was canceled due to s.writeErr.
 					// TODO(#51365): use a Context API to plumb this through req.ctx.
-					err = fmt.Errorf("%w: %v", ErrServerClosing, s.writeErr)
+					err = fmt.Errorf("%w: %w", ErrServerClosing, s.writeErr)
 				}
 			})
 			c.processResult("handleAsync", req, nil, err)
diff --git a/internal/jsonrpc2/conn_test.go b/internal/jsonrpc2/conn_test.go
new file mode 100644
index 00000000..afeb4c02
--- /dev/null
+++ b/internal/jsonrpc2/conn_test.go
@@ -0,0 +1,38 @@
+// Copyright 2025 The Go MCP SDK Authors. All rights reserved.
+// Use of this source code is governed by the license
+// that can be found in the LICENSE file.
+
+package jsonrpc2
+
+import (
+	"errors"
+	"io"
+	"testing"
+)
+
+// TestShuttingDownWrapsWriteError verifies that when a connection shuts down
+// because its write side failed, the returned error preserves the underlying
+// write error in its chain so callers can classify it with errors.Is (for
+// example, distinguishing io.EOF from a clean host disconnect versus a real
+// failure).
+func TestShuttingDownWrapsWriteError(t *testing.T) {
+	s := &inFlightState{writeErr: io.EOF}
+	err := s.shuttingDown(ErrServerClosing)
+	if !errors.Is(err, ErrServerClosing) {
+		t.Errorf("shuttingDown() error = %v, want it to wrap ErrServerClosing", err)
+	}
+	if !errors.Is(err, io.EOF) {
+		t.Errorf("shuttingDown() error = %v, want it to wrap io.EOF", err)
+	}
+}
+
+func TestShuttingDownWrapsReadError(t *testing.T) {
+	s := &inFlightState{readErr: io.EOF}
+	err := s.shuttingDown(ErrServerClosing)
+	if !errors.Is(err, ErrServerClosing) {
+		t.Errorf("shuttingDown() error = %v, want it to wrap ErrServerClosing", err)
+	}
+	if !errors.Is(err, io.EOF) {
+		t.Errorf("shuttingDown() error = %v, want it to wrap io.EOF", err)
+	}
+}