diff --git a/web/src/sessionReducer.test.ts b/web/src/sessionReducer.test.ts
index 1871ebc..5e29730 100644
--- a/web/src/sessionReducer.test.ts
+++ b/web/src/sessionReducer.test.ts
@@ -296,18 +296,17 @@ describe("history boundary replacement", () => {
     expect(next.replacementEvents.get(4)).toEqual(replacement);
   });
 
-  it("rejects invalid replacement targets", () => {
+  it("skips replacements whose target seq is absent", () => {
     const state = makeState();
-    expect(() =>
-      replaceHistoryBoundary(
-        state,
-        {
-          type: "turn/stop",
-          history_boundary: { anchor: "a", kind: "agent_turn" },
-        },
-        4,
-      ),
-    ).toThrow("matched 0");
+    const next = replaceHistoryBoundary(
+      state,
+      {
+        type: "turn/stop",
+        history_boundary: { anchor: "a", kind: "agent_turn" },
+      },
+      4,
+    );
+    expect(next).toBe(state);
   });
 
   it("rejects mismatched canonical identity", () => {
diff --git a/web/src/sessionReducer.ts b/web/src/sessionReducer.ts
index a3cb9f9..24b271a 100644
--- a/web/src/sessionReducer.ts
+++ b/web/src/sessionReducer.ts
@@ -858,6 +858,16 @@ export function replaceHistoryBoundary(
         (message.seq === seq ||
           (Array.isArray(message.seq) && message.seq.includes(seq))),
     );
+  if (matches.length === 0) {
+    // A replacement can reference a message this client doesn't have: a live
+    // boundary racing a still-streaming history load, or a boundary persisted
+    // under an older seq numbering. Dropping it degrades one message's
+    // replacement; throwing would wedge the whole session view on every load.
+    console.error(
+      `History replacement matched 0 messages at seq ${seq}; skipping`,
+    );
+    return s;
+  }
   if (matches.length !== 1)
     throw new Error(
       `History replacement matched ${matches.length} messages at seq ${seq}`,