Salary changes come with a new contract IME (unless the changes are in the bonus compensation). You can't force someone to sign a new contract (you can probably make them a sign or leave offer, but you can't make them sign) so you can't lower someone's base salary.

There is no need to have a contract. Many small businesses just hire people and give them a piece of paper saying what they will get or orally tell them how much they will get.

In the event there is a contract, unless the contract specifies compensation for terminating employment, the employer can always just terminate the employee for the reason of “this employee is no longer worth $x per hour/year to us”. Barring any other union agreements of course.

Can't you just fire an employee for whatever reason? Any change in contract is then equivalent to fire and hire.

Yeah OK, I hadn't considered that. Where I live (in the Netherlands) that would never fly.