diff --git a/gdb/ChangeLog b/gdb/ChangeLog
index 0de5a9d1597..5bceb92c379 100644
--- a/gdb/ChangeLog
+++ b/gdb/ChangeLog
@@ -1,3 +1,10 @@
+2021-03-25  Pedro Alves  <pedro@palves.net>
+
+	* remote.c
+	(remote_target::check_pending_events_prevent_wildcard_vcont):
+	Check whether the event's ptid is not null_ptid before looking up
+	the corresponding inferior.
+
 2021-03-24  Changbin Du  <changbin.du@gmail.com>
 
 	* riscv-tdep.c (riscv_breakpoint_kind_from_pc): Remove call to
diff --git a/gdb/remote.c b/gdb/remote.c
index ff1366ebc40..188f507febd 100644
--- a/gdb/remote.c
+++ b/gdb/remote.c
@@ -7190,14 +7190,16 @@ remote_target::check_pending_events_prevent_wildcard_vcont
 	  || event->ws.kind == TARGET_WAITKIND_VFORKED)
 	*may_global_wildcard = 0;
 
-      struct inferior *inf = find_inferior_ptid (this, event->ptid);
-
       /* This may be the first time we heard about this process.
 	 Regardless, we must not do a global wildcard resume, otherwise
 	 we'd resume this process too.  */
       *may_global_wildcard = 0;
-      if (inf != NULL)
-	get_remote_inferior (inf)->may_wildcard_vcont = false;
+      if (event->ptid != null_ptid)
+	{
+	  inferior *inf = find_inferior_ptid (this, event->ptid);
+	  if (inf != NULL)
+	    get_remote_inferior (inf)->may_wildcard_vcont = false;
+	}
     }
 }
 
diff --git a/gdb/testsuite/ChangeLog b/gdb/testsuite/ChangeLog
index 1bcdaeb69d5..65c322562cd 100644
--- a/gdb/testsuite/ChangeLog
+++ b/gdb/testsuite/ChangeLog
@@ -1,3 +1,9 @@
+2021-03-25  Pedro Alves  <pedro@palves.net>
+
+	* gdb.server/stop-reply-no-thread-multi.exp (run_test): Add
+	"target_non_stop" parameter and use it.
+	(top level): Add "maint set target-non-stop on/off" testing axis.
+
 2021-03-25  Andrew Burgess  <andrew.burgess@embecosm.com>
 
 	* lib/ada.exp (gnat_runtime_has_debug_info): Use -wrap with
diff --git a/gdb/testsuite/gdb.server/stop-reply-no-thread-multi.exp b/gdb/testsuite/gdb.server/stop-reply-no-thread-multi.exp
index 6350f5771e3..50cf10fe313 100644
--- a/gdb/testsuite/gdb.server/stop-reply-no-thread-multi.exp
+++ b/gdb/testsuite/gdb.server/stop-reply-no-thread-multi.exp
@@ -41,10 +41,15 @@ if { [build_executable "failed to prepare" $testfile $srcfile {debug pthreads}]
 }
 
 # Run the tests with different features of GDBserver disabled.
-proc run_test { disable_feature } {
+# TARGET_NON_STOP is passed to "maint set target-non-stop".
+proc run_test { target_non_stop disable_feature } {
     global binfile gdb_prompt decimal hex
+    global GDBFLAGS
 
-    clean_restart ${binfile}
+    save_vars { GDBFLAGS } {
+	append GDBFLAGS " -ex \"maint set target-non-stop $target_non_stop\""
+	clean_restart ${binfile}
+    }
 
     # Make sure we're disconnected, in case we're testing with an
     # extended-remote board, therefore already connected.
@@ -131,6 +136,11 @@ proc run_test { disable_feature } {
 #
 # T: Start GDBserver with the entire 'T' stop reply packet disabled,
 #    GDBserver will instead send the 'S' stop reply.
-foreach_with_prefix to_disable { "" Tthread T } {
-    run_test $to_disable
+#
+# Also test both all-stop and non-stop variants of the remote
+# protocol.
+foreach_with_prefix target-non-stop {"off" "on"} {
+    foreach_with_prefix to_disable { "" Tthread T } {
+	run_test ${target-non-stop} $to_disable
+    }
 }