diff --git a/libprocessgroup/cgroup_map.cpp b/libprocessgroup/cgroup_map.cpp
index 995162186..b3b497f68 100644
--- a/libprocessgroup/cgroup_map.cpp
+++ b/libprocessgroup/cgroup_map.cpp
@@ -336,8 +336,10 @@ CgroupMap::~CgroupMap() {
 }
 
 CgroupMap& CgroupMap::GetInstance() {
-    static CgroupMap instance;
-    return instance;
+    // Deliberately leak this object to avoid a race between destruction on
+    // process exit and concurrent access from another thread.
+    static auto* instance = new CgroupMap;
+    return *instance;
 }
 
 bool CgroupMap::LoadRcFile() {
diff --git a/libprocessgroup/task_profiles.cpp b/libprocessgroup/task_profiles.cpp
index f1fbcdebe..9362c0387 100644
--- a/libprocessgroup/task_profiles.cpp
+++ b/libprocessgroup/task_profiles.cpp
@@ -284,8 +284,10 @@ bool TaskProfile::ExecuteForTask(int tid) const {
 }
 
 TaskProfiles& TaskProfiles::GetInstance() {
-    static TaskProfiles instance;
-    return instance;
+    // Deliberately leak this object to avoid a race between destruction on
+    // process exit and concurrent access from another thread.
+    static auto* instance = new TaskProfiles;
+    return *instance;
 }
 
 TaskProfiles::TaskProfiles() {