Ending a relationship doesn’t require other person’s agreement or permission. It also doesn’t require special wordings.

If they keep contacting you, block them. Suicide threats are a manipulation but if you are concerned, I agree with Bill about calling the police. After they have police at their door every time, they’ll stop talking about suicide.

We all had relationships where other person wasn’t in agreement about the end. In fact my last ex, before I’ve met my husband, invented a story about him dying from cancer in hopes I come back. Didn’t have cancer and wasn’t dying