diff --git a/jupyterhub/proxy.py b/jupyterhub/proxy.py
index 5f706970..e30bb032 100644
--- a/jupyterhub/proxy.py
+++ b/jupyterhub/proxy.py
@@ -722,8 +722,9 @@ class ConfigurableHTTPProxy(Proxy):
         def _check_process():
             status = self.proxy_process.poll()
             if status is not None:
-                e = RuntimeError("Proxy failed to start with exit code %i" % status)
-                raise e from None
+                with self.proxy_process:
+                    e = RuntimeError("Proxy failed to start with exit code %i" % status)
+                    raise e from None
 
         for server in (public_server, api_server):
             for i in range(10):
diff --git a/jupyterhub/spawner.py b/jupyterhub/spawner.py
index c642f2c2..d356b9c7 100644
--- a/jupyterhub/spawner.py
+++ b/jupyterhub/spawner.py
@@ -1542,8 +1542,11 @@ class LocalProcessSpawner(Spawner):
         if self.proc is not None:
             status = self.proc.poll()
             if status is not None:
-                # clear state if the process is done
-                self.clear_state()
+                # handle SIGCHILD to avoid zombie processes
+                # and also close stdout/stderr file descriptors
+                with self.proc:
+                    # clear state if the process is done
+                    self.clear_state()
             return status
 
         # if we resumed from stored state,