diff --git a/homeassistant/components/sensor/recorder.py b/homeassistant/components/sensor/recorder.py
index be0feb7fa52..59f20a9ed25 100644
--- a/homeassistant/components/sensor/recorder.py
+++ b/homeassistant/components/sensor/recorder.py
@@ -4,6 +4,7 @@ from __future__ import annotations
 
 from collections import defaultdict
 from collections.abc import Callable, Iterable
+from contextlib import suppress
 import datetime
 from functools import partial
 import itertools
@@ -179,6 +180,14 @@ def _entity_history_to_float_and_state(
     return float_states
 
 
+def _is_numeric(state: State) -> bool:
+    """Return if the state is numeric."""
+    with suppress(ValueError, TypeError):
+        if (num_state := float(state.state)) is not None and math.isfinite(num_state):
+            return True
+    return False
+
+
 def _normalize_states(
     hass: HomeAssistant,
     old_metadatas: dict[str, tuple[int, StatisticMetaData]],
@@ -684,13 +693,14 @@ def _update_issues(
     """Update repair issues."""
     for state in sensor_states:
         entity_id = state.entity_id
+        numeric = _is_numeric(state)
         state_class = try_parse_enum(
             SensorStateClass, state.attributes.get(ATTR_STATE_CLASS)
         )
         state_unit = state.attributes.get(ATTR_UNIT_OF_MEASUREMENT)
 
         if metadata := metadatas.get(entity_id):
-            if state_class is None:
+            if numeric and state_class is None:
                 # Sensor no longer has a valid state class
                 report_issue(
                     "state_class_removed",
@@ -703,7 +713,7 @@ def _update_issues(
             metadata_unit = metadata[1]["unit_of_measurement"]
             converter = statistics.STATISTIC_UNIT_TO_UNIT_CONVERTER.get(metadata_unit)
             if not converter:
-                if not _equivalent_units({state_unit, metadata_unit}):
+                if numeric and not _equivalent_units({state_unit, metadata_unit}):
                     # The unit has changed, and it's not possible to convert
                     report_issue(
                         "units_changed",
@@ -717,7 +727,7 @@ def _update_issues(
                     )
                 else:
                     clear_issue("units_changed", entity_id)
-            elif state_unit not in converter.VALID_UNITS:
+            elif numeric and state_unit not in converter.VALID_UNITS:
                 # The state unit can't be converted to the unit in metadata
                 valid_units = (unit or "<None>" for unit in converter.VALID_UNITS)
                 valid_units_str = ", ".join(sorted(valid_units))
diff --git a/tests/components/sensor/test_recorder.py b/tests/components/sensor/test_recorder.py
index 77bb6e17f68..04e0a1b7de8 100644
--- a/tests/components/sensor/test_recorder.py
+++ b/tests/components/sensor/test_recorder.py
@@ -4332,6 +4332,26 @@ async def test_validate_unit_change_convertible(
     }
     await assert_validation_result(hass, client, expected, {"units_changed"})
 
+    # Unavailable state - empty response
+    hass.states.async_set(
+        "sensor.test",
+        "unavailable",
+        attributes={**attributes, "unit_of_measurement": "dogs"},
+        timestamp=now.timestamp(),
+    )
+    await async_recorder_block_till_done(hass)
+    await assert_validation_result(hass, client, {}, {})
+
+    # Unknown state - empty response
+    hass.states.async_set(
+        "sensor.test",
+        "unknown",
+        attributes={**attributes, "unit_of_measurement": "dogs"},
+        timestamp=now.timestamp(),
+    )
+    await async_recorder_block_till_done(hass)
+    await assert_validation_result(hass, client, {}, {})
+
     # Valid state - empty response
     hass.states.async_set(
         "sensor.test",
@@ -4531,6 +4551,26 @@ async def test_validate_statistics_unit_change_no_device_class(
     }
     await assert_validation_result(hass, client, expected, {"units_changed"})
 
+    # Unavailable state - empty response
+    hass.states.async_set(
+        "sensor.test",
+        "unavailable",
+        attributes={**attributes, "unit_of_measurement": "dogs"},
+        timestamp=now.timestamp(),
+    )
+    await async_recorder_block_till_done(hass)
+    await assert_validation_result(hass, client, {}, {})
+
+    # Unknown state - empty response
+    hass.states.async_set(
+        "sensor.test",
+        "unknown",
+        attributes={**attributes, "unit_of_measurement": "dogs"},
+        timestamp=now.timestamp(),
+    )
+    await async_recorder_block_till_done(hass)
+    await assert_validation_result(hass, client, {}, {})
+
     # Valid state - empty response
     hass.states.async_set(
         "sensor.test",
@@ -4627,6 +4667,20 @@ async def test_validate_statistics_state_class_removed(
     }
     await assert_validation_result(hass, client, expected, {"state_class_removed"})
 
+    # Unavailable state - empty response
+    hass.states.async_set(
+        "sensor.test", "unavailable", attributes=_attributes, timestamp=now.timestamp()
+    )
+    await async_recorder_block_till_done(hass)
+    await assert_validation_result(hass, client, {}, {})
+
+    # Unknown state - empty response
+    hass.states.async_set(
+        "sensor.test", "unknown", attributes=_attributes, timestamp=now.timestamp()
+    )
+    await async_recorder_block_till_done(hass)
+    await assert_validation_result(hass, client, {}, {})
+
 
 @pytest.mark.parametrize(
     ("units", "attributes", "unit"),
@@ -4871,6 +4925,26 @@ async def test_validate_statistics_unit_change_no_conversion(
     }
     await assert_validation_result(hass, client, expected, {"units_changed"})
 
+    # Unavailable state - empty response
+    hass.states.async_set(
+        "sensor.test",
+        "unavailable",
+        attributes={**attributes, "unit_of_measurement": unit2},
+        timestamp=now.timestamp(),
+    )
+    await async_recorder_block_till_done(hass)
+    await assert_validation_result(hass, client, {}, {})
+
+    # Unknown state - empty response
+    hass.states.async_set(
+        "sensor.test",
+        "unknown",
+        attributes={**attributes, "unit_of_measurement": unit2},
+        timestamp=now.timestamp(),
+    )
+    await async_recorder_block_till_done(hass)
+    await assert_validation_result(hass, client, {}, {})
+
     # Original unit - empty response
     hass.states.async_set(
         "sensor.test",