diff --git a/units/systemd-coredump.socket b/units/systemd-coredump.socket
index 922358fe5d..565374698d 100644
--- a/units/systemd-coredump.socket
+++ b/units/systemd-coredump.socket
@@ -11,6 +11,8 @@
 Description=Process Core Dump Socket
 Documentation=man:systemd-coredump(8)
 DefaultDependencies=no
+Before=shutdown.target
+Conflicts=shutdown.target
 
 [Socket]
 ListenSequentialPacket=/run/systemd/coredump