diff --git a/lib/http/2/connection.rb b/lib/http/2/connection.rb
index 6e74bc9..be77985 100644
--- a/lib/http/2/connection.rb
+++ b/lib/http/2/connection.rb
@@ -295,7 +295,12 @@ def receive(data)
             # PUSH_PROMISE and CONTINUATION frames MUST be minimally
             # processed to ensure a consistent compression state
             decode_headers(frame)
-            return if @state == :closed
+            # A GOAWAY moves the connection to :closed, but streams the peer
+            # promised to finish (id <= last_stream_id, already in @streams) can
+            # still complete (RFC 9113 Section 6.8). Only discard HEADERS that
+            # would open a NEW stream; a known stream's response must be
+            # delivered (its DATA frames already are - see the branch below).
+            return if @state == :closed && !@streams.key?(stream_id)
 
             stream = @streams[stream_id]
             if stream.nil?
diff --git a/spec/client_spec.rb b/spec/client_spec.rb
index 1d40f11..02722e5 100644
--- a/spec/client_spec.rb
+++ b/spec/client_spec.rb
@@ -309,6 +309,36 @@
       client << f.generate(push_promise_frame)
       expect(client.active_stream_count).to eq 1
     end
+
+    it "should deliver response headers for a stream the GOAWAY promised to finish" do
+      stream = client.new_stream # id 1
+      stream.send headers_frame
+
+      received = nil
+      stream.on(:headers) { |h| received = h }
+
+      # GOAWAY (last_stream: 2) covers this stream (id 1), so the server
+      # promised to finish it: its response, arriving after the GOAWAY, must
+      # still be delivered rather than dropped once the connection is :closed.
+      client << f.generate(goaway_frame)
+      client << f.generate(headers_frame.merge(payload: Compressor.new.encode(RESPONSE_HEADERS)))
+
+      expect(received).to eq(RESPONSE_HEADERS)
+    end
+
+    it "should drop response headers for a stream the GOAWAY refused" do
+      client << f.generate(goaway_frame) # last_stream: 2
+
+      opened = false
+      client.on(:stream) { opened = true }
+
+      # A stream beyond last_stream_id (id 5) was refused and never processed;
+      # its (unexpected) headers must not open a stream on the closed connection.
+      client << f.generate(headers_frame.merge(stream: 5, payload: Compressor.new.encode(RESPONSE_HEADERS)))
+
+      expect(opened).to be(false)
+      expect(client.active_stream_count).to eq 0
+    end
   end
 
   context "framing" do