diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index c0b9f3f429c10e..16d3c60cd1b488 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -593,6 +593,8 @@ def _read(self, size):
             else:
                 # Other decompressors have needs_input.
                 # decompress() can buffer data internally.
+                if self.cmp.eof:
+                    break
                 if self.cmp.needs_input:
                     cbuf = self.fileobj.read(self.bufsize)
                     if not cbuf:
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 2b4cf748dffc1a..479772b5c8a89a 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -1060,6 +1060,26 @@ def test_compare_members(self):
         finally:
             tar1.close()
 
+    def test_ignore_zeros_concatenated(self):
+        # gh-159643: reading past the end of the compressed data
+        # must not raise EOFError.
+        with self.open(tmpname, "wb") as fobj:
+            for name in ("a", "b"):
+                with tarfile.open(fileobj=fobj, mode="w") as tar:
+                    tar.addfile(tarfile.TarInfo(name))
+        with tarfile.open(tmpname, self.mode, ignore_zeros=True) as tar:
+            self.assertEqual(tar.getnames(), ["a", "b"])
+
+    def test_no_end_of_archive_blocks(self):
+        # gh-159643
+        tarinfo = tarfile.TarInfo("a")
+        tarinfo.size = 5
+        with self.open(tmpname, "wb") as fobj:
+            fobj.write(tarinfo.tobuf())
+            fobj.write(b"hello".ljust(tarfile.BLOCKSIZE, b"\0"))
+        with tarfile.open(tmpname, self.mode) as tar:
+            self.assertEqual(tar.getnames(), ["a"])
+
 class GzipStreamReadTest(GzipTest, GzipReadTestBase, StreamReadTest):
     pass
 
diff --git a/Misc/NEWS.d/next/Library/2026-10-17-19-33-13.gh-issue-159643.EJfe0IXetV.rst b/Misc/NEWS.d/next/Library/2026-10-17-19-33-13.gh-issue-159643.EJfe0IXetV.rst
new file mode 100644
index 00000000000000..a76e54de38cc4e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-10-17-19-33-13.gh-issue-159643.EJfe0IXetV.rst
@@ -0,0 +1,3 @@
+Fix :exc:`EOFError` raised by :mod:`tarfile` in stream mode with bz2, xz or
+zstd compression when reading past the end of the compressed data, for
+example with *ignore_zeros* or an archive without end-of-archive blocks.