Yes, they do.

> Specifically, if a third party sues a commercial customer for copyright infringement for using Microsoft’s Copilots or the output they generate, we will defend the customer and pay the amount of any adverse judgments or settlements that result from the lawsuit, as long as the customer used the guardrails and content filters we have built into our products.

https://blogs.microsoft.com/on-the-issues/2023/09/07/copilot...

> Under the updated terms, we will defend our customers from any copyright infringement claim made against them for their authorized use of our services or their outputs, and we will pay for any approved settlements or judgments that result.

https://www.anthropic.com/news/expanded-legal-protections-ap...

> Output indemnity. OpenAI’s indemnification obligations to Enterprise customers under the Agreement include claims that Customer’s use or distribution of Output infringes a third party’s intellectual property right.

https://openai.com/policies/service-terms/