The usual term is one-sided breakup — meaning one person wants the relationship to end more than the other, or the breakup happens without mutual agreement.

If you mean a breakup where one person is emotionally shattered, people might also say:

  • heartbroken breakup.
  • blindsided breakup , if it came as a surprise.
  • breakup with a broken heart , in plain language.

In online relationship breakdowns, the clearest match to your wording is one-sided breakup.

TL;DR: The name you’re probably looking for is **one-sided breakup**.