Location is absolutely the key here, and the earlier answer is right that it varies wildly. But I'd push back a bit on the framing - in many jurisdictions, an employer actually *can't* unilaterally cut your pay at all, even with notice. The legality hinges on whether you have an employment contract, what it says, and crucially, what jurisdiction you're in.
In most U.S. states, employment is at-will, which means employers can change pay terms going forward *if they give you proper notice and you stay* - but you then have the right to leave. What they can't do is breach an existing contract. If your contract specifies a salary for a set term, they're bound by it unless you mutually agree to modify it. Telling you "this is happening" isn't the same as getting your agreement. In many other countries - UK, Canada, Australia, parts of Europe - unilateral pay cuts are much more restricted and may constitute constructive dismissal or breach of contract. You'd typically have grounds to challenge it or resign and claim damages.
Your next move should be to pull your employment contract and read it carefully, then find out what labor laws apply where you work. If your contract doesn't explicitly allow unilateral pay adjustments, or if local law requires mutual consent to change terms, you have leverage. Document everything they've told you in writing (email them asking for clarification if needed). You might want to consult someone who actually knows your jurisdiction's employment law before deciding whether to accept this, push back, or move on.