diff --git a/libio/Makefile b/libio/Makefile
index 8720381fdc..6a507b67ea 100644
--- a/libio/Makefile
+++ b/libio/Makefile
@@ -91,6 +91,7 @@ tests = \
   tst-bz24051 \
   tst-bz24153 \
   tst-bz28828 \
+  tst-closeall \
   tst-eof \
   tst-ext \
   tst-ext2 \
diff --git a/libio/genops.c b/libio/genops.c
index 994ee9c0b1..99f5e80f20 100644
--- a/libio/genops.c
+++ b/libio/genops.c
@@ -119,7 +119,8 @@ _IO_link_in (struct _IO_FILE_plus *fp)
       if (_IO_vtable_offset ((FILE *) fp) == 0)
 	{
 	  fp->file._prevchain = (FILE **) &_IO_list_all;
-	  _IO_list_all->file._prevchain = &fp->file._chain;
+	  if (_IO_list_all != NULL)
+	    _IO_list_all->file._prevchain = &fp->file._chain;
 	}
       _IO_list_all = fp;
 #ifdef _IO_MTSAFE_IO
diff --git a/libio/tst-closeall.c b/libio/tst-closeall.c
new file mode 100644
index 0000000000..34f5246490
--- /dev/null
+++ b/libio/tst-closeall.c
@@ -0,0 +1,34 @@
+/* Test that opening a file when all files are closed does not crash (bug 31963)
+   Copyright (C) 2024 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include <support/check.h>
+#include <support/xstdio.h>
+
+static int
+do_test (void)
+{
+  xfclose (stdin);
+  xfclose (stdout);
+  xfclose (stderr);
+  FILE *f = xfopen ("/dev/null", "w");
+  fprintf (f, "final\n");
+  xfclose (f);
+  return 0;
+}
+
+#include <support/test-driver.c>