I've faced the same issue with latest MySQL Client (>5.7) while trying to connect lower versions of MySQL like 5.1.xx.
To avoid this issue (ERROR 2027 (HY000): Malformed packet), create a user with latest password authentication.
ex:
Login to MySQL 5.1.xx server and execute..
mysql> create user 'testuser'@'xx.xx.xxx.%' identified by 'testuser_Secret1';
Check if you have old_passwords enabled, then disable it for that session.
mysql> show session variables like 'old_passwords';
+-----------------+-------+
| Variable_name | Value |
+-----------------+-------+
| old_passwords | ON |
+-----------------+-------+
mysql> set session old_passwords = 0;
mysql> GRANT select on test.* TO 'testuser'@'xx.xx.xxx.%' identified by 'testuser_Secret1';
Verify password that should begin with "*SOMETHING1123SHOWNBELOW3034".
mysql> select user,host,password from mysql.user where user = 'testuser';
+-----------+---------------+-------------------------------------------+
| user | host | password |
+-----------+---------------+-------------------------------------------+
| testuser | xx.xx.xxx.% | *053CB27FDD2AE63F03D4A0B919E471E0E88DA262 |
+-----------+---------------+-------------------------------------------+
Now try logging from MySQL 5.7.xx Client and try to establish a connection to MySQL 5.1.xx server.
[testuser@localhost]# mysql -V
mysql Ver 14.14 Distrib 5.7.31, for Linux (x86_64) using EditLine wrapper
[testuser@localhost]# mysql -hxx.xx.xxx.xxx -u testuser -p
Enter password:
Welcome to the MySQL monitor. Commands end with ; or \g.
Your MySQL connection id is 1528853
Server version: 5.1.73-log Source distribution
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