diff --git a/src/nvim/event/proc.c b/src/nvim/event/proc.c
index 01fe62d132..eb8f2690a2 100644
--- a/src/nvim/event/proc.c
+++ b/src/nvim/event/proc.c
@@ -368,20 +368,27 @@ static void flush_stream(Proc *proc, RStream *stream)
     return;
   }
 
-  // Maximal remaining data size of terminated process is system
-  // buffer size.
-  // Also helps with a child process that keeps the output streams open. If it
-  // keeps sending data, we only accept as much data as the system buffer size.
-  // Otherwise this would block cleanup/teardown.
-  int system_buffer_size = 0;
-  int err = uv_recv_buffer_size((uv_handle_t *)&stream->s.uv.pipe,
-                                &system_buffer_size);
-  if (err) {
-    system_buffer_size = ARENA_BLOCK_SIZE;
+  size_t max_bytes = SIZE_MAX;
+#ifdef MSWIN
+  if (true) {
+#else
+  // Don't limit remaining data size of PTY master unless when tearing down, as it may
+  // have more remaining data than system buffer size (at least on Linux). #3030
+  if (proc->type != kProcTypePty || proc_is_tearing_down) {
+#endif
+    // Maximal remaining data size of terminated process is system buffer size.
+    // Also helps with a child process that keeps the output streams open. If it
+    // keeps sending data, we only accept as much data as the system buffer size.
+    // Otherwise this would block cleanup/teardown.
+    int system_buffer_size = 0;
+    // All members of the stream->s.uv union share the same address.
+    int err = uv_recv_buffer_size((uv_handle_t *)&stream->s.uv, &system_buffer_size);
+    if (err != 0) {
+      system_buffer_size = ARENA_BLOCK_SIZE;
+    }
+    max_bytes = stream->num_bytes + (size_t)system_buffer_size;
   }
 
-  size_t max_bytes = stream->num_bytes + (size_t)system_buffer_size;
-
   // Read remaining data.
   while (!stream->s.closed && stream->num_bytes < max_bytes) {
     // Remember number of bytes before polling
diff --git a/test/functional/fixtures/shell-test.c b/test/functional/fixtures/shell-test.c
index 08da133819..9eac77fc37 100644
--- a/test/functional/fixtures/shell-test.c
+++ b/test/functional/fixtures/shell-test.c
@@ -32,12 +32,14 @@ static void help(void)
   puts("  shell-test -t {prompt text} EXE \"prog args...\"");
   puts("    Prints \"{prompt text} $ progs args...\" to stderr.");
   puts("  shell-test REP N {text}");
-  puts("    Prints \"{lnr}: {text}\\n\" to stdout N times, taking N milliseconds.");
+  puts("    Prints \"{lnr}: {text}\\n\" to stdout N times, pausing every 100 lines.");
   puts("    Example:");
   puts("      shell-test REP 97 \"foo bar\"");
   puts("      0: foo bar");
   puts("      ...");
   puts("      96: foo bar");
+  puts("  shell-test REPFAST N {text}");
+  puts("    Like REP, but print as fast as possible and then exit immediately.");
   puts("  shell-test INTERACT");
   puts("    Prints \"interact $ \" to stderr, and waits for \"exit\" input.");
   puts("  shell-test EXIT {code}");
@@ -71,9 +73,10 @@ int main(int argc, char **argv)
       } else {
         fprintf(stderr, "ready $ ");
       }
-    } else if (strcmp(argv[1], "REP") == 0) {
+    } else if (strcmp(argv[1], "REP") == 0 || strcmp(argv[1], "REPFAST") == 0) {
+      bool fast = strcmp(argv[1], "REPFAST") == 0;
       if (argc != 4) {
-        fprintf(stderr, "REP expects exactly 3 arguments\n");
+        fprintf(stderr, "REP/REPFAST expects exactly 3 arguments\n");
         return 4;
       }
       int count = 0;
@@ -83,7 +86,7 @@ int main(int argc, char **argv)
       }
       for (int i = 0; i < count; i++) {
         printf("%d: %s\n", i, argv[3]);
-        if (i % 100 == 0) {
+        if (!fast && i % 100 == 0) {
           usleep(1000);  // Wait 1 ms (simulate typical output).
         }
         fflush(NULL);
diff --git a/test/functional/terminal/buffer_spec.lua b/test/functional/terminal/buffer_spec.lua
index f56f7377d0..7c6b76c08f 100644
--- a/test/functional/terminal/buffer_spec.lua
+++ b/test/functional/terminal/buffer_spec.lua
@@ -758,6 +758,25 @@ describe(':terminal buffer', function()
     ]])
   end)
 
+  it('does not drop data when job exits immediately after output #3030', function()
+    local screen = Screen.new(50, 7)
+    api.nvim_create_autocmd('TermClose', { command = 'let g:did_termclose = 1' })
+    fn.jobstart({ testprg('shell-test'), 'REPFAST', '20000', 'TEST' }, { term = true })
+    retry(nil, nil, function()
+      eq(1, api.nvim_get_var('did_termclose'))
+    end)
+    feed('i')
+    screen:expect([[
+      19996: TEST                                       |
+      19997: TEST                                       |
+      19998: TEST                                       |
+      19999: TEST                                       |
+                                                        |
+      [Process exited 0]^                                |
+      {5:-- TERMINAL --}                                    |
+    ]])
+  end)
+
   it('handles unprintable chars', function()
     local screen = Screen.new(50, 7)
     feed 'i'