diff --git a/states/statefile/testdata/roundtrip/v3-invalid-depends.in.tfstate b/states/statefile/testdata/roundtrip/v3-invalid-depends.in.tfstate
new file mode 100644
index 000000000..6943b6139
--- /dev/null
+++ b/states/statefile/testdata/roundtrip/v3-invalid-depends.in.tfstate
@@ -0,0 +1,42 @@
+{
+    "version": 3,
+    "terraform_version": "0.7.13",
+    "serial": 0,
+    "lineage": "f2968801-fa14-41ab-a044-224f3a4adf04",
+    "modules": [
+        {
+            "path": [
+                "root"
+            ],
+            "outputs": {
+                "numbers": {
+                    "sensitive": false,
+                    "type": "string",
+                    "value": "0,1"
+                }
+            },
+            "resources": {
+                "null_resource.bar": {
+                    "type": "null_resource",
+                    "depends_on": [
+                        "null_resource.valid",
+                        "null_resource.1invalid"
+                    ],
+                    "primary": {
+                        "id": "5388490630832483079",
+                        "attributes": {
+                            "id": "5388490630832483079",
+                            "triggers.%": "1",
+                            "triggers.whaaat": "0,1"
+                        },
+                        "meta": {},
+                        "tainted": false
+                    },
+                    "deposed": [],
+                    "provider": ""
+                }
+            },
+            "depends_on": []
+        }
+    ]
+}
\ No newline at end of file
diff --git a/states/statefile/testdata/roundtrip/v3-invalid-depends.out.tfstate b/states/statefile/testdata/roundtrip/v3-invalid-depends.out.tfstate
new file mode 100644
index 000000000..5fdef34f6
--- /dev/null
+++ b/states/statefile/testdata/roundtrip/v3-invalid-depends.out.tfstate
@@ -0,0 +1,33 @@
+{
+    "version": 4,
+    "serial": 0,
+    "lineage": "f2968801-fa14-41ab-a044-224f3a4adf04",
+    "terraform_version": "0.7.13",
+    "outputs": {
+        "numbers": {
+            "type": "string",
+            "value": "0,1"
+        }
+    },
+    "resources": [
+        {
+            "mode": "managed",
+            "type": "null_resource",
+            "name": "bar",
+            "provider": "provider.null",
+            "instances": [
+                {
+                    "schema_version": 0,
+                    "attributes_flat": {
+                        "id": "5388490630832483079",
+                        "triggers.%": "1",
+                        "triggers.whaaat": "0,1"
+                    },
+                    "depends_on": [
+                        "null_resource.valid"
+                    ]
+                }
+            ]
+        }
+    ]
+}
\ No newline at end of file
diff --git a/states/statefile/version3_upgrade.go b/states/statefile/version3_upgrade.go
index 943e0f45c..64c3c1afb 100644
--- a/states/statefile/version3_upgrade.go
+++ b/states/statefile/version3_upgrade.go
@@ -3,6 +3,7 @@ package statefile
 import (
 	"encoding/json"
 	"fmt"
+	"log"
 	"strconv"
 	"strings"
 
@@ -299,13 +300,33 @@ func upgradeInstanceObjectV3ToV4(rsOld *resourceStateV2, isOld *instanceStateV2,
 		}
 	}
 
-	dependencies := make([]string, len(rsOld.Dependencies))
-	for i, v := range rsOld.Dependencies {
+	dependencies := make([]string, 0, len(rsOld.Dependencies))
+	for _, v := range rsOld.Dependencies {
 		depStr, err := parseLegacyDependency(v)
 		if err != nil {
-			return nil, fmt.Errorf("invalid dependency reference %q: %s", v, err)
+			// We just drop invalid dependencies on the floor here, because
+			// they tend to get left behind in Terraform 0.11 when resources
+			// are renamed or moved between modules and there's no automatic
+			// way to fix them here. In practice it shouldn't hurt to miss
+			// a few dependency edges in the state because a subsequent plan
+			// will run a refresh walk first and re-synchronize the
+			// dependencies with the configuration.
+			//
+			// There is one rough edges where this can cause an incorrect
+			// result, though: If the first command the user runs after
+			// upgrading to Terraform 0.12 uses -refresh=false and thus
+			// prevents the dependency reorganization from occurring _and_
+			// that initial plan discovered "orphaned" resources (not present
+			// in configuration any longer) then when the plan is applied the
+			// destroy ordering will be incorrect for the instances of those
+			// resources. We expect that is a rare enough situation that it
+			// isn't a big deal, and even when it _does_ occur it's common for
+			// the apply to succeed anyway unless many separate resources with
+			// complex inter-dependencies are all orphaned at once.
+			log.Printf("statefile: ignoring invalid dependency address %q while upgrading from state version 3 to version 4: %s", v, err)
+			continue
 		}
-		dependencies[i] = depStr
+		dependencies = append(dependencies, depStr)
 	}
 
 	return &instanceObjectStateV4{