diff --git a/Library/Homebrew/cleanup.rb b/Library/Homebrew/cleanup.rb
index bbdf2710b3..8d0c9e9f44 100644
--- a/Library/Homebrew/cleanup.rb
+++ b/Library/Homebrew/cleanup.rb
@@ -600,6 +600,7 @@ module Homebrew
       ObserverPathnameExtension.reset_counts!
 
       dirs = []
+      children_count = {}
 
       Keg::MUST_EXIST_SUBDIRECTORIES.each do |dir|
         next unless dir.directory?
@@ -612,21 +613,24 @@ module Homebrew
 
               if dry_run?
                 puts "Would remove (broken link): #{path}"
+                children_count[path.dirname] -= 1 if children_count.key?(path.dirname)
               else
                 path.unlink
               end
             end
           elsif path.directory? && Keg::MUST_EXIST_SUBDIRECTORIES.exclude?(path)
             dirs << path
+            children_count[path] = path.children.length if dry_run?
           end
         end
       end
 
       dirs.reverse_each do |d|
-        if dry_run? && d.children.empty?
-          puts "Would remove (empty directory): #{d}"
-        else
+        if !dry_run?
           d.rmdir_if_possible
+        elsif children_count[d].zero?
+          puts "Would remove (empty directory): #{d}"
+          children_count[d.dirname] -= 1 if children_count.key?(d.dirname)
         end
       end
 
diff --git a/Library/Homebrew/test/cleanup_spec.rb b/Library/Homebrew/test/cleanup_spec.rb
index b4a09a8721..b166364594 100644
--- a/Library/Homebrew/test/cleanup_spec.rb
+++ b/Library/Homebrew/test/cleanup_spec.rb
@@ -95,6 +95,76 @@ RSpec.describe Homebrew::Cleanup do
     end
   end
 
+  describe "::prune_prefix_symlinks_and_directories" do
+    let(:lib) { HOMEBREW_PREFIX/"lib" }
+
+    before do
+      lib.mkpath
+    end
+
+    it "keeps required empty directories" do
+      cleanup.prune_prefix_symlinks_and_directories
+      expect(lib).to exist
+      expect(lib.children).to be_empty
+    end
+
+    it "removes broken symlinks" do
+      FileUtils.ln_s lib/"foo", lib/"bar"
+      FileUtils.touch lib/"baz"
+
+      cleanup.prune_prefix_symlinks_and_directories
+      expect(lib).to exist
+      expect(lib.children).to eq([lib/"baz"])
+    end
+
+    it "removes empty directories" do
+      dir = lib/"test"
+      dir.mkpath
+      file = lib/"keep/file"
+      file.dirname.mkpath
+      FileUtils.touch file
+
+      cleanup.prune_prefix_symlinks_and_directories
+      expect(dir).not_to exist
+      expect(file).to exist
+    end
+
+    context "when nested directories exist with only broken symlinks" do
+      let(:dir) { HOMEBREW_PREFIX/"lib/foo" }
+      let(:child_dir) { dir/"bar" }
+      let(:grandchild_dir) { child_dir/"baz" }
+      let(:broken_link) { dir/"broken" }
+      let(:link_to_broken_link) { child_dir/"another-broken" }
+
+      before do
+        grandchild_dir.mkpath
+        FileUtils.ln_s dir/"missing", broken_link
+        FileUtils.ln_s broken_link, link_to_broken_link
+      end
+
+      it "removes broken symlinks and resulting empty directories" do
+        cleanup.prune_prefix_symlinks_and_directories
+        expect(dir).not_to exist
+      end
+
+      it "doesn't remove anything and only prints removal steps if `dry_run` is true" do
+        expect do
+          described_class.new(dry_run: true).prune_prefix_symlinks_and_directories
+        end.to output(<<~EOS).to_stdout
+          Would remove (broken link): #{link_to_broken_link}
+          Would remove (broken link): #{broken_link}
+          Would remove (empty directory): #{grandchild_dir}
+          Would remove (empty directory): #{child_dir}
+          Would remove (empty directory): #{dir}
+        EOS
+
+        expect(broken_link).to be_a_symlink
+        expect(link_to_broken_link).to be_a_symlink
+        expect(grandchild_dir).to exist
+      end
+    end
+  end
+
   specify "::cleanup_formula" do
     f1 = Class.new(Testball) do
       version "1.0"