From the mysql client:
show processlist;
+-----+------+-----------------+---------------+---------+-------+-------+------------------+
| Id | User | Host | db | Command | Time | State | Info |
+-----+------+-----------------+---------------+---------+-------+-------+------------------+
| 2 | root | localhost:6509 | so_gibberish2 | Sleep | 105 | | NULL |
| 3 | root | localhost:6510 | so_gibberish2 | Sleep | 105 | | NULL |
| 820 | root | localhost:40286 | stackoverflow | Sleep | 13457 | | NULL |
| 821 | root | localhost:40287 | stackoverflow | Sleep | 966 | | NULL |
| 827 | root | localhost:42254 | so_gibberish2 | Query | 0 | init | show processlist |
| 831 | root | localhost:44036 | stackoverflow | Sleep | 230 | | NULL |
+-----+------+-----------------+---------------+---------+-------+-------+------------------+
select connection_id();
+-----------------+
| connection_id() |
+-----------------+
| 827 |
+-----------------+
Now hit [x] as you say to client the mysql client that ran the above.
Below is from Mysql Workbench:
show processlist;
+-----+------+-----------------+---------------+---------+-------+-------+------------------+
| Id | User | Host | db | Command | Time | State | Info |
+-----+------+-----------------+---------------+---------+-------+-------+------------------+
| 2 | root | localhost:6509 | so_gibberish2 | Sleep | 105 | | NULL |
| 3 | root | localhost:6510 | so_gibberish2 | Sleep | 105 | | NULL |
| 820 | root | localhost:40286 | stackoverflow | Sleep | 13457 | | NULL |
| 821 | root | localhost:40287 | stackoverflow | Sleep | 966 | | NULL |
+-----+------+-----------------+---------------+---------+-------+-------+------------------+
select connection_id();
+-----------------+
| connection_id() |
+-----------------+
| 3 |
+-----------------+
So the closing of a program naturally closes any open sockets it has.
Honestly, the latter output looks more like:

But I always use the mysql client for output formatting for tables which would throw off the results. So there you have it as an image.