diff --git a/python/pyspark/accumulators.py b/python/pyspark/accumulators.py
index 59f7856688ee..5d3f8bda04c0 100644
--- a/python/pyspark/accumulators.py
+++ b/python/pyspark/accumulators.py
@@ -266,12 +266,37 @@ def handle(self) -> None:
         auth_token = self.server.auth_token  # type: ignore[attr-defined]
 
         def poll(func: Callable[[], bool]) -> None:
+            poller = None
+            if os.name == "posix":
+                # On posix systems use poll to avoid problems with file descriptor
+                # numbers above 1024.
+                poller = select.poll()
+                poller.register(self.rfile, select.POLLIN)
+
             while not self.server.server_shutdown:  # type: ignore[attr-defined]
                 # Poll every 1 second for new data -- don't block in case of shutdown.
-                r, _, _ = select.select([self.rfile], [], [], 1)
-                if self.rfile in r and func():
+                r: set | list
+                if poller is not None:
+                    r = set()
+                    # Unlike select, poll timeout is in millis.
+                    for fd, event in poller.poll(1000):
+                        if event & (select.POLLIN | select.POLLHUP):
+                            # Data can be read (for POLLHUP peer hang up, so reads will return
+                            # 0 bytes, in which case we want to break out - this is consistent
+                            # with how select behaves).
+                            r.add(fd)
+                        else:
+                            # Could be POLLERR or POLLNVAL (select would raise in this case).
+                            raise PySparkRuntimeError(f"Polling error - event {event} on fd {fd}")
+                else:
+                    # If poll is not available, use select.
+                    r, _, _ = select.select([self.rfile.fileno()], [], [], 1)
+                if self.rfile.fileno() in r and func():
                     break
 
+            if poller is not None:
+                poller.unregister(self.rfile)
+
         def accum_updates() -> bool:
             num_updates = read_int(self.rfile)
             for _ in range(num_updates):
diff --git a/python/pyspark/daemon.py b/python/pyspark/daemon.py
index 7495569ecfda..5744fcefa436 100644
--- a/python/pyspark/daemon.py
+++ b/python/pyspark/daemon.py
@@ -30,6 +30,7 @@
 from signal import SIGHUP, SIGTERM, SIGCHLD, SIG_DFL, SIG_IGN, SIGINT
 
 from pyspark.serializers import read_int, write_int, write_with_length, UTF8Deserializer
+from pyspark.errors import PySparkRuntimeError
 
 
 def compute_real_exit_code(exit_code):
@@ -173,16 +174,22 @@ def handle_sigterm(*args):
             poller.register(listen_sock, select.POLLIN)
 
         while True:
+            ready_fds: set | list
             if poller is not None:
-                ready_fds = [fd_reverse_map[fd] for fd, _ in poller.poll(1000)]
-            else:
-                try:
-                    ready_fds = select.select([0, listen_sock], [], [], 1)[0]
-                except select.error as ex:
-                    if ex[0] == EINTR:
-                        continue
+                ready_fds = set()
+                # Unlike select, poll timeout is in millis.
+                for fd, event in poller.poll(1000):
+                    if event & (select.POLLIN | select.POLLHUP):
+                        # Data can be read (for POLLHUP peer hang up, so reads will return
+                        # 0 bytes, in which case we want to break out - this is consistent
+                        # with how select behaves).
+                        ready_fds.add(fd_reverse_map[fd])
                     else:
-                        raise
+                        # Could be POLLERR or POLLNVAL (select would raise in this case).
+                        raise PySparkRuntimeError(f"Polling error - event {event} on fd {fd}")
+            else:
+                # If poll is not available, use select.
+                ready_fds = select.select([0, listen_sock], [], [], 1)[0]
 
             if 0 in ready_fds:
                 try: