Sharing a database connection with multiple modules
If you are creating a database wrapper, why not make a lib out of the wrapper and stick it into a lib directory that other modules/classes can import? So, your Users class would be in a directory structure like this:

project/
    account.py
    lib/
        database.py
    user.py
    zombie.py


Your database.py would look something like:

import pymysql

class Database:    
    @staticmethod
    def connect_dbs():
        econ = _mdb.connect(host='db.com',
                            user='user', passwd=pass,
                            db='db', charset='utf8')
        return econ


Then, in the user.py, you'd simply do an import like:

from .lib.database import Database as MyDatabase


Then, to get the connection, something along the lines of:

my_connection = MyDatabase.connect_dbs()


EDIT: As an example, see this repl.it:

class Database:
    connection = None

    def __init__(self):
        print "Instantiating!"

    def connect_dbs(self):
        if self.connection is not None:
            return self.connection

        self.connection = 1
        return self.connection


class User:
    db = None

    def __init__(self):
        self.db = Database()

    def save_user(self):
        print self.db.connect_dbs()

U = User()
for i in range(30):
    U.save_user() # Only instantiates the connection once, then reuses it 30x