diff --git a/gdb/ChangeLog b/gdb/ChangeLog
index 9d63febea0..7892202168 100644
--- a/gdb/ChangeLog
+++ b/gdb/ChangeLog
@@ -1,3 +1,12 @@
+2020-01-10  Tankut Baris Aktemur  <tankut.baris.aktemur@intel.com>
+	    Pedro Alves	 <palves@redhat.com>
+
+	* remote.c (remote_target::remote_parse_stop_reply) <W/X packets>:
+	If no process is specified, return null_ptid instead of
+	inferior_ptid.
+	(remote_target::wait_as): Handle TARGET_WAITKIND_EXITED /
+	TARGET_WAITKIND_SIGNALLED with no pid.
+
 2020-01-10  Pedro Alves  <palves@redhat.com>
 
 	* remote.c (first_remote_resumed_thread): New.
diff --git a/gdb/remote.c b/gdb/remote.c
index fa940dff72..ffdeede7af 100644
--- a/gdb/remote.c
+++ b/gdb/remote.c
@@ -7441,7 +7441,6 @@ Packet: '%s'\n"),
     case 'W':		/* Target exited.  */
     case 'X':
       {
-	int pid;
 	ULONGEST value;
 
 	/* GDB used to accept only 2 hex chars here.  Stubs should
@@ -7465,8 +7464,9 @@ Packet: '%s'\n"),
 	      event->ws.value.sig = GDB_SIGNAL_UNKNOWN;
 	  }
 
-	/* If no process is specified, assume inferior_ptid.  */
-	pid = inferior_ptid.pid ();
+	/* If no process is specified, return null_ptid, and let the
+	   caller figure out the right process to use.  */
+	int pid = 0;
 	if (*p == '\0')
 	  ;
 	else if (*p == ';')
@@ -7842,8 +7842,16 @@ remote_target::wait_as (ptid_t ptid, target_waitstatus *status, int options)
 	event_ptid = first_remote_resumed_thread ();
     }
   else
-    /* A process exit.  Invalidate our notion of current thread.  */
-    record_currthread (rs, minus_one_ptid);
+    {
+      /* A process exit.  Invalidate our notion of current thread.  */
+      record_currthread (rs, minus_one_ptid);
+      /* It's possible that the packet did not include a pid.  */
+      if (event_ptid == null_ptid)
+	event_ptid = first_remote_resumed_thread ();
+      /* EVENT_PTID could still be NULL_PTID.  Double-check.  */
+      if (event_ptid == null_ptid)
+	event_ptid = magic_null_ptid;
+    }
 
   return event_ptid;
 }
diff --git a/gdb/testsuite/ChangeLog b/gdb/testsuite/ChangeLog
index 4b38c214da..52d52d15f6 100644
--- a/gdb/testsuite/ChangeLog
+++ b/gdb/testsuite/ChangeLog
@@ -1,3 +1,9 @@
+2020-01-10  Tankut Baris Aktemur  <tankut.baris.aktemur@intel.com>
+	    Pedro Alves	 <palves@redhat.com>
+
+	* gdb.server/connect-without-multi-process.exp: Also test
+	continuing to end.
+
 2020-01-10  Pedro Alves  <palves@redhat.com>
 
 	* gdb.base/remote-exec-file.exp: New file.
diff --git a/gdb/testsuite/gdb.server/connect-without-multi-process.exp b/gdb/testsuite/gdb.server/connect-without-multi-process.exp
index 6c7d162492..123089260d 100644
--- a/gdb/testsuite/gdb.server/connect-without-multi-process.exp
+++ b/gdb/testsuite/gdb.server/connect-without-multi-process.exp
@@ -14,7 +14,7 @@
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
 
 # Check that we can connect to GDBserver with the multiprocess
-# extensions disabled, and run to main.
+# extensions disabled, run to main, and finish the process.
 
 load_lib gdbserver-support.exp
 
@@ -52,6 +52,11 @@ proc do_test {multiprocess} {
 	"target $gdbserver_protocol"
 
     gdb_test "continue" "main .*" "continue to main"
+
+    # The W/X packets do not include the PID of the exiting process
+    # without the multi-process extensions.  Check that we handle
+    # process exit correctly in that case.
+    gdb_continue_to_end
 }
 
 foreach multiprocess { "off" "auto" } {