diff --git a/cmd/cue/cmd/testdata/script/export_issue3511.txtar b/cmd/cue/cmd/testdata/script/export_issue3511.txtar
new file mode 100644
index 00000000000..a4a3f2482a7
--- /dev/null
+++ b/cmd/cue/cmd/testdata/script/export_issue3511.txtar
@@ -0,0 +1,34 @@
+
+env CUE_EXPERIMENT=evalv3=1
+exec cue export
+cmp stdout out/stdout
+
+-- cue.mod/module.cue --
+module: "module.test/foo"
+language: version: "v0.9.0"
+
+-- main.cue --
+package p
+
+import "module.test/foo/imported@v0"
+
+items: [imported.List]
+-- imported/imported.cue --
+package imported
+
+Namespace: "default"
+
+List: [...{namespace: Namespace}]
+
+List: [{name: "kube-api-server"}]
+-- out/stdout --
+{
+    "items": [
+        [
+            {
+                "name": "kube-api-server",
+                "namespace": "default"
+            }
+        ]
+    ]
+}
diff --git a/internal/core/adt/context.go b/internal/core/adt/context.go
index d6b867a70b7..65bb2716a45 100644
--- a/internal/core/adt/context.go
+++ b/internal/core/adt/context.go
@@ -229,6 +229,12 @@ type OpContext struct {
 	// structural cycle errors.
 	vertex *Vertex
 
+	// list of vertices that need to be finalized.
+	// TODO: remove this again once we have a proper way of detecting references
+	// across optional boundaries in hasAncestorV3. We can probably do this
+	// with an optional depth counter.
+	toFinalize []*Vertex
+
 	// These fields are used associate scratch fields for computing closedness
 	// of a Vertex. These fields could have been included in StructInfo (like
 	// Tomabechi's unification algorithm), but we opted for an indirection to
diff --git a/internal/core/adt/share.go b/internal/core/adt/share.go
index 2f9c4816f52..099a72bcc6b 100644
--- a/internal/core/adt/share.go
+++ b/internal/core/adt/share.go
@@ -58,10 +58,20 @@ func (n *nodeContext) finalizeSharing() {
 		n.sharedID.cc.decDependent(n.ctx, SHARED, n.node.cc())
 		n.sharedID.cc = nil
 	}
-	if n.isShared {
-		v := n.node.BaseValue.(*Vertex)
+	if !n.isShared {
+		return
+	}
+	switch v := n.node.BaseValue.(type) {
+	case *Vertex:
+		if n.sharedID.CycleType == NoCycle {
+			v.Finalize(n.ctx)
+		} else if !v.isFinal() {
+			// TODO: ideally we just handle cycles in optional chains directly,
+			// rather than relying on this mechanism. This requires us to add
+			// a mechanism to detect that.
+			n.ctx.toFinalize = append(n.ctx.toFinalize, v)
+		}
 		if v.Parent == n.node.Parent {
-			v.unify(n.ctx, needTasksDone, finalize)
 			if !v.Rooted() && v.MayAttach() {
 				n.isShared = false
 				n.node.Arcs = v.Arcs
@@ -71,6 +81,10 @@ func (n *nodeContext) finalizeSharing() {
 				n.node.HasEllipsis = v.HasEllipsis
 			}
 		}
+	case *Bottom:
+		// An error trumps sharing. We can leave it as is.
+	default:
+		panic("unreachable")
 	}
 }
 
diff --git a/internal/core/adt/unify.go b/internal/core/adt/unify.go
index 69f51339ae0..dcb04f7cfbb 100644
--- a/internal/core/adt/unify.go
+++ b/internal/core/adt/unify.go
@@ -130,6 +130,19 @@ func (v *Vertex) unify(c *OpContext, needs condition, mode runMode) bool {
 		}()
 	}
 
+	if c.evalDepth == 0 {
+		defer func() {
+			// This loop processes nodes that need to be evaluated, but should be
+			// evaluated outside of the stack to avoid structural cycle detection.
+			// See comment at toFinalize.
+			a := c.toFinalize
+			c.toFinalize = c.toFinalize[:0]
+			for _, x := range a {
+				x.Finalize(c)
+			}
+		}()
+	}
+
 	if mode == ignore {
 		return false
 	}