diff --git a/source/libs/function/src/builtinsimpl.c b/source/libs/function/src/builtinsimpl.c
index dcf58759b01755f545f5b70f1b811218995fd2c2..f396f6e60948a3a669fc20ff2f453a692faa409e 100644
--- a/source/libs/function/src/builtinsimpl.c
+++ b/source/libs/function/src/builtinsimpl.c
@@ -2795,6 +2795,8 @@ int32_t firstFunction(SqlFunctionCtx* pCtx) {
   // All null data column, return directly.
   if (pInput->colDataAggIsSet && (pInput->pColumnDataAgg[0]->numOfNull == pInput->totalRows)) {
     ASSERT(pInputCol->hasNull == true);
+    // save selectivity value for column consisted of all null values
+    firstlastSaveTupleData(pCtx->pSrcBlock, pInput->startRowIndex, pCtx, pInfo);
     return 0;
   }
 
@@ -2871,7 +2873,10 @@ int32_t firstFunction(SqlFunctionCtx* pCtx) {
     }
   }
 #endif
-
+  if (numOfElems == 0) {
+    // save selectivity value for column consisted of all null values
+    firstlastSaveTupleData(pCtx->pSrcBlock, pInput->startRowIndex, pCtx, pInfo);
+  }
   SET_VAL(pResInfo, numOfElems, 1);
   return TSDB_CODE_SUCCESS;
 }
@@ -2892,6 +2897,8 @@ int32_t lastFunction(SqlFunctionCtx* pCtx) {
   // All null data column, return directly.
   if (pInput->colDataAggIsSet && (pInput->pColumnDataAgg[0]->numOfNull == pInput->totalRows)) {
     ASSERT(pInputCol->hasNull == true);
+    // save selectivity value for column consisted of all null values
+    firstlastSaveTupleData(pCtx->pSrcBlock, pInput->startRowIndex, pCtx, pInfo);
     return 0;
   }
 
@@ -2952,7 +2959,10 @@ int32_t lastFunction(SqlFunctionCtx* pCtx) {
     }
   }
 #endif
-
+  if (numOfElems == 0) {
+    // save selectivity value for column consisted of all null values
+    firstlastSaveTupleData(pCtx->pSrcBlock, pInput->startRowIndex, pCtx, pInfo);
+  }
   SET_VAL(pResInfo, numOfElems, 1);
   return TSDB_CODE_SUCCESS;
 }
diff --git a/source/libs/function/src/tudf.c b/source/libs/function/src/tudf.c
index 5d894783fbada48446406db1d60da8121d1a690d..3f472b53a026de186bbab2e70d37997b2b2fda44 100644
--- a/source/libs/function/src/tudf.c
+++ b/source/libs/function/src/tudf.c
@@ -1805,6 +1805,7 @@ int32_t doTeardownUdf(UdfcFuncHandle handle) {
 
   if (session->udfUvPipe == NULL) {
     fnError("tear down udf. pipe to udfd does not exist. udf name: %s", session->udfName);
+    taosMemoryFree(session);
     return TSDB_CODE_UDF_PIPE_NO_PIPE;
   }
 
@@ -1823,6 +1824,7 @@ int32_t doTeardownUdf(UdfcFuncHandle handle) {
   udfcRunUdfUvTask(task, UV_TASK_DISCONNECT);
 
   fnInfo("tear down udf. udf name: %s, udf func handle: %p", session->udfName, handle);
+  //TODO: synchronization refactor between libuv event loop and request thread
   if (session->udfUvPipe != NULL && session->udfUvPipe->data != NULL) {
     SClientUvConn *conn = session->udfUvPipe->data;
     conn->session = NULL;