diff --git a/lib/puma/plugin/solid_queue.rb b/lib/puma/plugin/solid_queue.rb
index 8a7aea28b..3fff5d417 100644
--- a/lib/puma/plugin/solid_queue.rb
+++ b/lib/puma/plugin/solid_queue.rb
@@ -129,5 +129,9 @@ def puma_dead?
 
     def log(...)
       log_writer.log(...)
+    rescue Errno::EIO, Errno::EPIPE, Errno::EBADF
+      # The controlling terminal can disappear, or the output pipe close, before
+      # the monitor thread shuts down the child process. Keep shutdown moving
+      # even when logging cannot.
     end
 end
diff --git a/test/unit/puma_plugin_test.rb b/test/unit/puma_plugin_test.rb
new file mode 100644
index 000000000..24325ef8f
--- /dev/null
+++ b/test/unit/puma_plugin_test.rb
@@ -0,0 +1,28 @@
+# frozen_string_literal: true
+
+require "test_helper"
+require "puma/plugin/solid_queue"
+
+class PumaPluginTest < ActiveSupport::TestCase
+  class ClosedOutputLogWriter
+    def initialize(error)
+      @error = error
+    end
+
+    def log(...)
+      raise @error
+    end
+  end
+
+  [ Errno::EIO, Errno::EPIPE, Errno::EBADF ].each do |error|
+    test "monitor still stops the process when shutdown logging fails with #{error}" do
+      plugin = Puma::Plugins.find("solid_queue").new
+      plugin.instance_variable_set(:@log_writer, ClosedOutputLogWriter.new(error))
+
+      plugin.stubs(:puma_dead?).returns(true)
+      Process.expects(:kill).with(:INT, Process.pid)
+
+      plugin.send(:monitor, :puma_dead?, "Detected Puma has gone away, stopping Solid Queue...")
+    end
+  end
+end