scikit-learn
diff --git a/‎doc/whats_new/v0.24.rst
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diff --git a/‎sklearn/cross_decomposition/_pls.py
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diff --git a/‎sklearn/cross_decomposition/tests/test_pls.py
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@@ -25,6 +25,10 @@ Changelog
 - |Fix| Fixed a regression in :class:`cross_decomposition.CCA`. :pr:`19646`
   by `Thomas Fan`_.
 
+- |Fix| :class:`cross_decomposition.PLSRegression` raises warning for
+  constant y residuals instead of a `StopIteration` error. :pr:`19922`
+  by `Thomas Fan`_.
+
 :mod:`sklearn.decomposition`
 ............................
 
 
@@ -52,7 +52,11 @@ def _get_first_singular_vectors_power_method(X, Y, mode="A", max_iter=500,
     """
 
     eps = np.finfo(X.dtype).eps
-    y_score = next(col for col in Y.T if np.any(np.abs(col) > eps))
+    try:
+        y_score = next(col for col in Y.T if np.any(np.abs(col) > eps))
+    except StopIteration as e:
+        raise StopIteration("Y residual is constant") from e
+
     x_weights_old = 100  # init to big value for first convergence check
 
     if mode == 'B':
@@ -256,10 +260,17 @@ def fit(self, X, Y):
                 Yk_mask = np.all(np.abs(Yk) < 10 * Y_eps, axis=0)
                 Yk[:, Yk_mask] = 0.0
 
-                x_weights, y_weights, n_iter_ = \
-                    _get_first_singular_vectors_power_method(
-                        Xk, Yk, mode=self.mode, max_iter=self.max_iter,
-                        tol=self.tol, norm_y_weights=norm_y_weights)
+                try:
+                    x_weights, y_weights, n_iter_ = \
+                        _get_first_singular_vectors_power_method(
+                            Xk, Yk, mode=self.mode, max_iter=self.max_iter,
+                            tol=self.tol, norm_y_weights=norm_y_weights)
+                except StopIteration as e:
+                    if str(e) != "Y residual is constant":
+                        raise
+                    warnings.warn(f"Y residual is constant at iteration {k}")
+                    break
+
                 self.n_iter_.append(n_iter_)
 
             elif self.algorithm == "svd":
 
@@ -565,3 +565,18 @@ def test_loadings_converges():
 
     # Loadings converges to reasonable values
     assert np.all(np.abs(cca.x_loadings_) < 1)
+
+
+def test_pls_constant_y():
+    """Checks warning when y is constant. Non-regression test for #19831"""
+    rng = np.random.RandomState(42)
+    x = rng.rand(100, 3)
+    y = np.zeros(100)
+
+    pls = PLSRegression()
+
+    msg = "Y residual is constant at iteration"
+    with pytest.warns(UserWarning, match=msg):
+        pls.fit(x, y)
+
+    assert_allclose(pls.x_rotations_, 0)