diff --git a/libpod/stats_linux.go b/libpod/stats_linux.go
index c65d2583e1..502ed70e68 100644
--- a/libpod/stats_linux.go
+++ b/libpod/stats_linux.go
@@ -132,6 +132,9 @@ func getOnlineCPUs(container *Container) (int, error) {
 	}
 	var cpuSet unix.CPUSet
 	if err := unix.SchedGetaffinity(ctrPID, &cpuSet); err != nil {
+		if errors.Is(err, unix.ESRCH) {
+			return -1, fmt.Errorf("container %s exited while obtaining online cpus: %w", container.Name(), errors.Join(err, define.ErrCtrStopped))
+		}
 		return -1, fmt.Errorf("failed to obtain Container %s online cpus: %w", container.Name(), err)
 	}
 	return cpuSet.Count(), nil
diff --git a/pkg/api/handlers/compat/containers_stats.go b/pkg/api/handlers/compat/containers_stats.go
index 95e158b75b..1d02dece63 100644
--- a/pkg/api/handlers/compat/containers_stats.go
+++ b/pkg/api/handlers/compat/containers_stats.go
@@ -3,7 +3,9 @@
 package compat
 
 import (
+	"bytes"
 	"encoding/json"
+	"errors"
 	"fmt"
 	"net/http"
 	"time"
@@ -45,20 +47,17 @@ func StatsContainer(w http.ResponseWriter, r *http.Request) {
 
 	stats, err := ctnr.GetContainerStats(nil)
 	if err != nil {
-		utils.InternalServerError(w, fmt.Errorf("failed to obtain Container %s stats: %w", name, err))
+		err = fmt.Errorf("failed to obtain Container %s stats: %w", name, err)
+		utils.Error(w, statsErrorStatus(err), err)
 		return
 	}
-
-	coder := json.NewEncoder(w)
-	// Write header and content type.
-	w.WriteHeader(http.StatusOK)
-	w.Header().Set("Content-Type", "application/json")
-	if flusher, ok := w.(http.Flusher); ok {
-		flusher.Flush()
+	onlineCPUs, err := libpod.GetOnlineCPUs(ctnr)
+	if err != nil {
+		utils.Error(w, statsErrorStatus(err), err)
+		return
 	}
+	wroteContent := false
 
-	// Set up JSON encoder for streaming.
-	coder.SetEscapeHTML(true)
 	var preRead time.Time
 	var preCPUStats CPUStats
 	if query.Stream {
@@ -66,12 +65,6 @@ func StatsContainer(w http.ResponseWriter, r *http.Request) {
 		preCPUStats = getPreCPUStats(stats)
 	}
 
-	onlineCPUs, err := libpod.GetOnlineCPUs(ctnr)
-	if err != nil {
-		utils.InternalServerError(w, err)
-		return
-	}
-
 streamLabel: // A label to flatten the scope
 	select {
 	case <-r.Context().Done():
@@ -80,11 +73,20 @@ streamLabel: // A label to flatten the scope
 	default:
 		stats, err = ctnr.GetContainerStats(stats)
 		if err != nil {
-			logrus.Errorf("Unable to get container stats: %v", err)
+			if wroteContent {
+				logrus.Errorf("Unable to get container stats: %v", err)
+			} else {
+				utils.Error(w, statsErrorStatus(err), err)
+			}
 			return
 		}
 		s, err := statsContainerJSON(ctnr, stats, preCPUStats, onlineCPUs)
 		if err != nil {
+			if wroteContent {
+				logrus.Errorf("Unable to build container stats response: %v", err)
+			} else {
+				utils.Error(w, statsErrorStatus(err), err)
+			}
 			return
 		}
 		s.Stats.PreRead = preRead
@@ -96,10 +98,25 @@ streamLabel: // A label to flatten the scope
 			jsonOut = DockerStatsJSON(s)
 		}
 
-		if err := coder.Encode(jsonOut); err != nil {
-			logrus.Errorf("Unable to encode stats: %v", err)
+		var chunk bytes.Buffer
+		if err := json.NewEncoder(&chunk).Encode(jsonOut); err != nil {
+			if wroteContent {
+				logrus.Errorf("Unable to encode stats: %v", err)
+			} else {
+				utils.InternalServerError(w, err)
+			}
 			return
 		}
+
+		// Do not commit a successful response until the complete sample has
+		// been collected and encoded. For a stream, each write is one complete
+		// sample, so an error can only truncate the stream between samples.
+		w.Header().Set("Content-Type", "application/json")
+		if _, err := w.Write(chunk.Bytes()); err != nil {
+			logrus.Errorf("Unable to write stats: %v", err)
+			return
+		}
+		wroteContent = true
 		if flusher, ok := w.(http.Flusher); ok {
 			flusher.Flush()
 		}
@@ -112,11 +129,24 @@ streamLabel: // A label to flatten the scope
 		bits, err := json.Marshal(s.CPUStats)
 		if err != nil {
 			logrus.Errorf("Unable to marshal cpu stats: %q", err)
+			return
 		}
 		if err := json.Unmarshal(bits, &preCPUStats); err != nil {
 			logrus.Errorf("Unable to unmarshal previous stats: %q", err)
+			return
 		}
 		time.Sleep(defaultStatsPeriod)
 		goto streamLabel
 	}
 }
+
+func statsErrorStatus(err error) int {
+	switch {
+	case errors.Is(err, define.ErrNoSuchCtr), errors.Is(err, define.ErrCtrRemoved):
+		return http.StatusNotFound
+	case errors.Is(err, define.ErrCtrStopped), errors.Is(err, define.ErrCtrStateInvalid), errors.Is(err, define.ErrNoCgroups):
+		return http.StatusConflict
+	default:
+		return http.StatusInternalServerError
+	}
+}
diff --git a/pkg/api/handlers/compat/containers_stats_test.go b/pkg/api/handlers/compat/containers_stats_test.go
new file mode 100644
index 0000000000..b294566370
--- /dev/null
+++ b/pkg/api/handlers/compat/containers_stats_test.go
@@ -0,0 +1,36 @@
+//go:build !remote && (linux || freebsd)
+
+package compat
+
+import (
+	"errors"
+	"fmt"
+	"net/http"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"go.podman.io/podman/v6/libpod/define"
+)
+
+func TestStatsErrorStatus(t *testing.T) {
+	testCases := []struct {
+		name string
+		err  error
+		want int
+	}{
+		{name: "not found", err: define.ErrNoSuchCtr, want: http.StatusNotFound},
+		{name: "removed", err: define.ErrCtrRemoved, want: http.StatusNotFound},
+		{name: "stopped", err: define.ErrCtrStopped, want: http.StatusConflict},
+		{name: "invalid state", err: define.ErrCtrStateInvalid, want: http.StatusConflict},
+		{name: "no cgroups", err: define.ErrNoCgroups, want: http.StatusConflict},
+		{name: "wrapped stopped", err: fmt.Errorf("collecting stats: %w", define.ErrCtrStopped), want: http.StatusConflict},
+		{name: "internal", err: errors.New("permission denied"), want: http.StatusInternalServerError},
+	}
+
+	for _, testCase := range testCases {
+		t.Run(testCase.name, func(t *testing.T) {
+			got := statsErrorStatus(testCase.err)
+			assert.Equal(t, testCase.want, got)
+		})
+	}
+}
diff --git a/pkg/api/server/register_containers.go b/pkg/api/server/register_containers.go
index 5cd368efce..cdf3f609fb 100644
--- a/pkg/api/server/register_containers.go
+++ b/pkg/api/server/register_containers.go
@@ -417,6 +417,8 @@ func (s *APIServer) registerContainersHandlers(r *mux.Router) error {
 	//       type: object
 	//   404:
 	//     $ref: "#/responses/containerNotFound"
+	//   409:
+	//     $ref: "#/responses/conflictError"
 	//   500:
 	//     $ref: "#/responses/internalError"
 	r.HandleFunc(VersionedPath("/containers/{name}/stats"), s.StreamBufferedAPIHandler(compat.StatsContainer)).Methods(http.MethodGet)
diff --git a/test/apiv2/19-stats.at b/test/apiv2/19-stats.at
index 4431ab8fbb..43a9a2e8a0 100644
--- a/test/apiv2/19-stats.at
+++ b/test/apiv2/19-stats.at
@@ -33,3 +33,11 @@ podman network rm testnet2
 podman run -dt --name testctr3 --memory-reservation=10m $IMAGE top &>/dev/null
 t GET libpod/containers/testctr3/stats?stream=false 200
 podman rm -f testctr3
+
+# A stopped container cannot provide CPU stats. The handler must report the
+# error before committing a successful response.
+podman run --name stopped-stats $IMAGE true
+t GET libpod/containers/stopped-stats/stats?stream=false 409 \
+    .cause="container is stopped" \
+    .response=409
+podman rm stopped-stats
diff --git a/winmake.ps1 b/winmake.ps1
index c8b56950af..be0ae13c93 100644
--- a/winmake.ps1
+++ b/winmake.ps1
@@ -66,7 +66,8 @@ function Make-Clean {
 
 function Local-Unit {
     Build-Ginkgo
-    $skippackages = 'hack,internal\domain\infra\abi,internal\domain\infra\tunnel,libpod\lock\shm,pkg\api\handlers\libpod,pkg\api\handlers\utils,pkg\bindings,'
+    # The compat stats handler depends on the local libpod stats implementation, which is not built on Windows.
+    $skippackages = 'hack,internal\domain\infra\abi,internal\domain\infra\tunnel,libpod\lock\shm,pkg\api\handlers\compat,pkg\api\handlers\libpod,pkg\api\handlers\utils,pkg\bindings,'
     $skippackages += 'pkg\domain\infra\abi,pkg\emulation,pkg\machine\apple,pkg\machine\applehv,pkg\machine\e2e,pkg\machine\libkrun,'
     $skippackages += 'pkg\machine\proxyenv,pkg\machine\qemu,pkg\specgen\generate,pkg\systemd,test\e2e,test\utils,cmd\rootlessport,'
     $skippackages += 'pkg\pidhandle'