The emerging "agentic web" envisions large populations of autonomous agents coordinating, transacting, and delegating across open networks. Yet many agent communication and commerce protocols treat agents as low-cost identities, despite the empirical reality that LLM agents remain unreliable, hallucinated, manipulable, and vulnerable to prompt-injection and tool-abuse. A natural response is "agents-at-stake": binding economically meaningful, slashable collateral to persistent identities and adjudicating misbehavior with verifiable evidence. However, heterogeneous tasks make universal verification brittle and centralization-prone, while traditional reputation struggles under rapid model drift and opaque internal states. We propose a protocol-native alternative: insured agents. Specialized insurer agents post stake on behalf of operational agents in exchange for premiums, and receive privileged, privacy-preserving audit access via TEEs to assess claims. A hierarchical insurer market calibrates stake through pricing, decentralizes verification via competitive underwriting, and yields incentive-compatible dispute resolution.