how wsrep_local_index is defined or could be changed?
The wsrep_local_index does not change due to desync mode. You most likely restart the node, this process does change the local index.

Here is the log of the process to show that it does not change:

MariaDB [(none)]&gt; show global status like 'wsrep_local_index';
+-------------------+-------+
| Variable_name     | Value |
+-------------------+-------+
| wsrep_local_index | 0     |
+-------------------+-------+
1 row in set (0.002 sec)

MariaDB [(none)]&gt; set global wsrep_desync=1;
Query OK, 0 rows affected (0.001 sec)

MariaDB [(none)]&gt; show global status like 'wsrep_local_index';
+-------------------+-------+
| Variable_name     | Value |
+-------------------+-------+
| wsrep_local_index | 0     |
+-------------------+-------+
1 row in set (0.002 sec)

MariaDB [(none)]&gt; set global wsrep_desync=0;
Query OK, 0 rows affected (0.000 sec)

MariaDB [(none)]&gt; show global status like 'wsrep_local_index';
+-------------------+-------+
| Variable_name     | Value |
+-------------------+-------+
| wsrep_local_index | 0     |
+-------------------+-------+
1 row in set (0.002 sec)